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      <id>a36bba8a-891e-4766-990f-f1a646f3b911</id>
      <revision>10</revision>
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    <calculation>
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      <exponentialThreshold>5</exponentialThreshold>
      <fractions>decimal</fractions>
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    <pageModel active="true" printAreas="true" simpleEqualsOnly="false" printBackgroundImages="true">
      <paper id="9" orientation="Portrait" width="827" height="1169" />
      <margins left="11" right="19" top="11" bottom="39" />
      <header alignment="Center" color="#a9a9a9">&amp;[DATE] &amp;[TIME] - &amp;[FILENAME]</header>
      <footer alignment="Center" color="#a9a9a9">&amp;[PAGENUM] / &amp;[COUNT]</footer>
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      <assembly name="EFI for SMath Studio" version="1.0.4977.35617" guid="91a20d24-c30b-4774-9b1b-4d502a80420f" />
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  <region id="0" left="9" top="18" width="152" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="eng">
      <p bold="true">Special Functions</p>
    </text>
    <text lang="ger">
      <p bold="true">Specialfunktionen</p>
    </text>
  </region>
  <region id="1" left="450" top="18" width="135" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p href="Plugin Cephes Mathematical Library.sm">Cephes Math Lib</p>
    </text>
  </region>
  <region id="2" left="450" top="36" width="176" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p href="Plugin EFI for SMath Studio.sm">EFI for SMath Studio</p>
    </text>
  </region>
  <region id="3" left="9" top="45" width="333" height="40" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="rus">
      <p>A Mathematical library for MathCad v1.2
by: Giuseppe Borzì</p>
    </text>
  </region>
  <region id="4" left="450" top="54" width="70" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="eng">
      <p href="Plugin index.sm">Plugins</p>
    </text>
    <text lang="ger">
      <p href="Plugin index.sm">Anwendungserweiterungen (Plugins)</p>
    </text>
  </region>
  <region id="5" left="450" top="72" width="78" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="eng">
      <p href="Handbook.sm">Contents</p>
    </text>
    <text lang="ger">
      <p href="Handbook.sm">Inhalt</p>
    </text>
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    <math decimalPlaces="2">
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        <e type="operand">π</e>
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    <math decimalPlaces="2">
      <input>
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        <e type="operand">π</e>
        <e type="operator" args="1">-</e>
        <e type="operand">i</e>
        <e type="operand">e</e>
        <e type="operator" args="2">*</e>
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    </math>
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    <math decimalPlaces="2">
      <input>
        <e type="operand">a</e>
        <e type="operand">e</e>
        <e type="operator" args="2">:</e>
      </input>
    </math>
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    <math decimalPlaces="2">
      <input>
        <e type="operand">b</e>
        <e type="operand">0.569</e>
        <e type="operator" args="2">:</e>
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    </math>
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    <math decimalPlaces="2">
      <input>
        <e type="operand">k</e>
        <e type="operand">3</e>
        <e type="operator" args="2">:</e>
      </input>
    </math>
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  <region id="11" left="360" top="108" width="43" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <math decimalPlaces="2">
      <input>
        <e type="operand">x</e>
        <e type="operand">π</e>
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  <region id="12" left="0" top="135" width="606" height="56" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="rus">
      <p>1) Unscaled and scaled Bessel functions of the first and second kind 
of real order and complex argument; unscaled and scaled Hankel functions 
of real order and complex argument.</p>
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        <e type="operand">z</e>
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        <e type="operand">0.06</e>
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        <e type="operand">0.06</e>
        <e type="operand">i</e>
        <e type="operator" args="2">*</e>
        <e type="operator" args="2">+</e>
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    </math>
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        <e type="operand">z</e>
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        <e type="operand">0.06</e>
        <e type="operator" args="1">-</e>
        <e type="operand">0.06</e>
        <e type="operand">i</e>
        <e type="operator" args="2">*</e>
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      <input>
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        <e type="operand">z</e>
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        <e type="operand">0.83</e>
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        <e type="operand">z</e>
        <e type="function" preserve="true" args="2">H2e</e>
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        <e type="operand">0.13</e>
        <e type="operand">0.12</e>
        <e type="operand">i</e>
        <e type="operator" args="2">*</e>
        <e type="operator" args="2">-</e>
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    <math decimalPlaces="2">
      <input>
        <e type="operand">v</e>
        <e type="operand">z</e>
        <e type="function" preserve="true" args="2">Jv</e>
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        <e type="operand">0.96</e>
        <e type="operator" args="1">-</e>
        <e type="operand">0.91</e>
        <e type="operand">i</e>
        <e type="operator" args="2">*</e>
        <e type="operator" args="2">+</e>
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    </math>
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    <math decimalPlaces="2">
      <input>
        <e type="operand">v</e>
        <e type="operand">z</e>
        <e type="function" preserve="true" args="2">Yv</e>
      </input>
      <result action="numeric">
        <e type="operand">0.85</e>
        <e type="operator" args="1">-</e>
        <e type="operand">0.95</e>
        <e type="operand">i</e>
        <e type="operator" args="2">*</e>
        <e type="operator" args="2">-</e>
      </result>
    </math>
  </region>
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    <math decimalPlaces="2">
      <input>
        <e type="operand">v</e>
        <e type="operand">z</e>
        <e type="function" preserve="true" args="2">H1v</e>
      </input>
      <result action="numeric">
        <e type="operand">0.01</e>
        <e type="operator" args="1">-</e>
        <e type="operand">0.06</e>
        <e type="operand">i</e>
        <e type="operator" args="2">*</e>
        <e type="operator" args="2">+</e>
      </result>
    </math>
  </region>
  <region id="20" left="306" top="297" width="209" height="26" color="#000000" bgColor="#ffffff" fontSize="10">
    <math decimalPlaces="2">
      <input>
        <e type="operand">v</e>
        <e type="operand">z</e>
        <e type="function" preserve="true" args="2">H2v</e>
      </input>
      <result action="numeric">
        <e type="operand">1.91</e>
        <e type="operator" args="1">-</e>
        <e type="operand">1.76</e>
        <e type="operand">i</e>
        <e type="operator" args="2">*</e>
        <e type="operator" args="2">+</e>
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    </math>
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  <region id="21" left="0" top="351" width="507" height="40" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="rus">
      <p>2)Unscaled and scaled modified Bessel functions of the first 
and second kind of real order and complex argument.</p>
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  <region id="22" left="0" top="405" width="191" height="26" color="#000000" bgColor="#ffffff" fontSize="10">
    <math decimalPlaces="2">
      <input>
        <e type="operand">v</e>
        <e type="operand">z</e>
        <e type="function" preserve="true" args="2">Iv</e>
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      <result action="numeric">
        <e type="operand">1.64</e>
        <e type="operand">0.62</e>
        <e type="operand">i</e>
        <e type="operator" args="2">*</e>
        <e type="operator" args="2">+</e>
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    </math>
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      <input>
        <e type="operand">v</e>
        <e type="operand">z</e>
        <e type="function" preserve="true" args="2">Kv</e>
      </input>
      <result action="numeric">
        <e type="operand">0.52</e>
        <e type="operand">5.49</e>
        <e type="operand">i</e>
        <e type="operator" args="2">*</e>
        <e type="operator" args="2">+</e>
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    </math>
  </region>
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    <math decimalPlaces="2">
      <input>
        <e type="operand">v</e>
        <e type="operand">z</e>
        <e type="function" preserve="true" args="2">Ie</e>
      </input>
      <result action="numeric">
        <e type="operand">0.07</e>
        <e type="operand">0.03</e>
        <e type="operand">i</e>
        <e type="operator" args="2">*</e>
        <e type="operator" args="2">+</e>
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    </math>
  </region>
  <region id="25" left="306" top="432" width="200" height="26" color="#000000" bgColor="#ffffff" fontSize="10">
    <math decimalPlaces="2">
      <input>
        <e type="operand">v</e>
        <e type="operand">z</e>
        <e type="function" preserve="true" args="2">Ke</e>
      </input>
      <result action="numeric">
        <e type="operand">0.12</e>
        <e type="operator" args="1">-</e>
        <e type="operand">0.21</e>
        <e type="operand">i</e>
        <e type="operator" args="2">*</e>
        <e type="operator" args="2">-</e>
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    </math>
  </region>
  <region id="26" left="0" top="495" width="528" height="40" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="rus">
      <p>3) Spherical Bessel functions of the first and second kind 
of real order and complex argument; spherical Hankel functions.</p>
    </text>
  </region>
  <region id="27" left="0" top="576" width="200" height="26" color="#000000" bgColor="#ffffff" fontSize="10">
    <math decimalPlaces="2">
      <input>
        <e type="operand">v</e>
        <e type="operand">z</e>
        <e type="function" preserve="true" args="2">jv</e>
      </input>
      <result action="numeric">
        <e type="operand">0.38</e>
        <e type="operator" args="1">-</e>
        <e type="operand">0.45</e>
        <e type="operand">i</e>
        <e type="operator" args="2">*</e>
        <e type="operator" args="2">+</e>
      </result>
    </math>
  </region>
  <region id="28" left="306" top="576" width="200" height="26" color="#000000" bgColor="#ffffff" fontSize="10">
    <math decimalPlaces="2">
      <input>
        <e type="operand">v</e>
        <e type="operand">z</e>
        <e type="function" preserve="true" args="2">yv</e>
      </input>
      <result action="numeric">
        <e type="operand">0.47</e>
        <e type="operator" args="1">-</e>
        <e type="operand">0.42</e>
        <e type="operand">i</e>
        <e type="operator" args="2">*</e>
        <e type="operator" args="2">-</e>
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    </math>
  </region>
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    <math decimalPlaces="2">
      <input>
        <e type="operand">v</e>
        <e type="operand">z</e>
        <e type="function" preserve="true" args="2">h1v</e>
      </input>
      <result action="numeric">
        <e type="operand">0.04</e>
        <e type="operand">0.02</e>
        <e type="operand">i</e>
        <e type="operator" args="2">*</e>
        <e type="operator" args="2">-</e>
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    </math>
  </region>
  <region id="30" left="306" top="603" width="201" height="26" color="#000000" bgColor="#ffffff" fontSize="10">
    <math decimalPlaces="2">
      <input>
        <e type="operand">v</e>
        <e type="operand">z</e>
        <e type="function" preserve="true" args="2">h2v</e>
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      <result action="numeric">
        <e type="operand">0.8</e>
        <e type="operator" args="1">-</e>
        <e type="operand">0.92</e>
        <e type="operand">i</e>
        <e type="operator" args="2">*</e>
        <e type="operator" args="2">+</e>
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    </math>
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    <text lang="rus">
      <p>4) Unscaled and scaled Airy functions and their first derivatives 
of complex argument; Struve function.</p>
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      <input>
        <e type="operand">z</e>
        <e type="function" preserve="true" args="1">Ai</e>
      </input>
      <result action="numeric">
        <e type="operand">14.18</e>
        <e type="operator" args="1">-</e>
        <e type="operand">24.44</e>
        <e type="operand">i</e>
        <e type="operator" args="2">*</e>
        <e type="operator" args="2">+</e>
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    </math>
  </region>
  <region id="33" left="306" top="693" width="192" height="26" color="#000000" bgColor="#ffffff" fontSize="10">
    <math decimalPlaces="2">
      <input>
        <e type="operand">z</e>
        <e type="function" preserve="true" args="1">Bi</e>
      </input>
      <result action="numeric">
        <e type="operand">24.44</e>
        <e type="operator" args="1">-</e>
        <e type="operand">14.18</e>
        <e type="operand">i</e>
        <e type="operator" args="2">*</e>
        <e type="operator" args="2">-</e>
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    </math>
  </region>
  <region id="34" left="0" top="729" width="192" height="26" color="#000000" bgColor="#ffffff" fontSize="10">
    <math decimalPlaces="2">
      <input>
        <e type="operand">z</e>
        <e type="function" preserve="true" args="1">Aip</e>
      </input>
      <result action="numeric">
        <e type="operand">55.09</e>
        <e type="operand">10.37</e>
        <e type="operand">i</e>
        <e type="operator" args="2">*</e>
        <e type="operator" args="2">+</e>
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    </math>
  </region>
  <region id="35" left="306" top="729" width="201" height="26" color="#000000" bgColor="#ffffff" fontSize="10">
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      <input>
        <e type="operand">z</e>
        <e type="function" preserve="true" args="1">Bip</e>
      </input>
      <result action="numeric">
        <e type="operand">10.37</e>
        <e type="operator" args="1">-</e>
        <e type="operand">55.08</e>
        <e type="operand">i</e>
        <e type="operator" args="2">*</e>
        <e type="operator" args="2">+</e>
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    </math>
  </region>
  <region id="36" left="0" top="756" width="167" height="26" color="#000000" bgColor="#ffffff" fontSize="10">
    <math decimalPlaces="2">
      <input>
        <e type="operand">z</e>
        <e type="function" preserve="true" args="1">Ae</e>
      </input>
      <result action="numeric">
        <e type="operand">0.16</e>
        <e type="operand">0.12</e>
        <e type="operand">i</e>
        <e type="operator" args="2">*</e>
        <e type="operator" args="2">-</e>
      </result>
    </math>
  </region>
  <region id="37" left="306" top="756" width="168" height="26" color="#000000" bgColor="#ffffff" fontSize="10">
    <math decimalPlaces="2">
      <input>
        <e type="operand">z</e>
        <e type="function" preserve="true" args="1">Be</e>
      </input>
      <result action="numeric">
        <e type="operand">0.17</e>
        <e type="operator" args="1">-</e>
        <e type="operand">0.1</e>
        <e type="operand">i</e>
        <e type="operator" args="2">*</e>
        <e type="operator" args="2">-</e>
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    </math>
  </region>
  <region id="38" left="0" top="792" width="185" height="26" color="#000000" bgColor="#ffffff" fontSize="10">
    <math decimalPlaces="2">
      <input>
        <e type="operand">z</e>
        <e type="function" preserve="true" args="1">Aep</e>
      </input>
      <result action="numeric">
        <e type="operand">0.32</e>
        <e type="operator" args="1">-</e>
        <e type="operand">0.23</e>
        <e type="operand">i</e>
        <e type="operator" args="2">*</e>
        <e type="operator" args="2">-</e>
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    </math>
  </region>
  <region id="39" left="306" top="792" width="185" height="26" color="#000000" bgColor="#ffffff" fontSize="10">
    <math decimalPlaces="2">
      <input>
        <e type="operand">z</e>
        <e type="function" preserve="true" args="1">Bep</e>
      </input>
      <result action="numeric">
        <e type="operand">0.07</e>
        <e type="operator" args="1">-</e>
        <e type="operand">0.39</e>
        <e type="operand">i</e>
        <e type="operator" args="2">*</e>
        <e type="operator" args="2">+</e>
      </result>
    </math>
  </region>
  <region id="40" left="0" top="819" width="163" height="26" color="#000000" bgColor="#ffffff" fontSize="10">
    <math decimalPlaces="2">
      <input>
        <e type="operand">v</e>
        <e type="operand">x</e>
        <e type="function" preserve="true" args="2">Struve</e>
      </input>
      <result action="numeric">
        <e type="operand">0.36</e>
      </result>
    </math>
  </region>
  <region id="41" left="0" top="864" width="572" height="104" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="rus">
      <p>5) Logarithm of gamma function, beta function and logarithm 
of beta function of complex arguments; reciprocal of gamma function, 
binomial coefficient,Psi function, incomplete gamma function, 
complemented incomplete gamma function, inverse of incomplete 
complemented gamma function, incomplete beta function and inverse 
incomplete beta function.</p>
    </text>
  </region>
  <region id="42" left="0" top="990" width="185" height="26" color="#000000" bgColor="#ffffff" fontSize="10">
    <math decimalPlaces="2">
      <input>
        <e type="operand">z</e>
        <e type="function" preserve="true" args="1">lgam</e>
      </input>
      <result action="numeric">
        <e type="operand">7.74</e>
        <e type="operator" args="1">-</e>
        <e type="operand">7.7</e>
        <e type="operand">i</e>
        <e type="operator" args="2">*</e>
        <e type="operator" args="2">-</e>
      </result>
    </math>
  </region>
  <region id="43" left="324" top="990" width="168" height="26" color="#000000" bgColor="#ffffff" fontSize="10">
    <math decimalPlaces="2">
      <input>
        <e type="operand">z</e>
        <e type="function" preserve="true" args="1">Psi</e>
      </input>
      <result action="numeric">
        <e type="operand">1.51</e>
        <e type="operand">2.5</e>
        <e type="operand">i</e>
        <e type="operator" args="2">*</e>
        <e type="operator" args="2">+</e>
      </result>
    </math>
  </region>
  <region id="44" left="0" top="1017" width="168" height="26" color="#000000" bgColor="#ffffff" fontSize="10">
    <math decimalPlaces="2">
      <input>
        <e type="operand">a</e>
        <e type="operand">z</e>
        <e type="operator" args="2">-</e>
        <e type="operand">z</e>
        <e type="function" preserve="true" args="2">beta</e>
      </input>
      <result action="numeric">
        <e type="operand">0.01</e>
      </result>
    </math>
  </region>
  <region id="45" left="0" top="1053" width="246" height="26" color="#000000" bgColor="#ffffff" fontSize="10">
    <math decimalPlaces="2">
      <input>
        <e type="operand">a</e>
        <e type="operand">z</e>
        <e type="operator" args="2">-</e>
        <e type="operand">z</e>
        <e type="function" preserve="true" args="2">lbeta</e>
      </input>
      <result action="numeric">
        <e type="operand">4.3</e>
        <e type="operator" args="1">-</e>
        <e type="operand">12.38</e>
        <e type="operand">i</e>
        <e type="operator" args="2">*</e>
        <e type="operator" args="2">-</e>
      </result>
    </math>
  </region>
  <region id="46" left="0" top="1089" width="123" height="26" color="#000000" bgColor="#ffffff" fontSize="10">
    <math decimalPlaces="2">
      <input>
        <e type="operand">x</e>
        <e type="function" preserve="true" args="1">rgam</e>
      </input>
      <result action="numeric">
        <e type="operand">0.44</e>
      </result>
    </math>
  </region>
  <region id="47" left="207" top="1089" width="147" height="26" color="#000000" bgColor="#ffffff" fontSize="10">
    <math decimalPlaces="2">
      <input>
        <e type="operand">a</e>
        <e type="operand">x</e>
        <e type="function" preserve="true" args="2">igam</e>
      </input>
      <result action="numeric">
        <e type="operand">0.67</e>
      </result>
    </math>
  </region>
  <region id="48" left="405" top="1089" width="155" height="26" color="#000000" bgColor="#ffffff" fontSize="10">
    <math decimalPlaces="2">
      <input>
        <e type="operand">a</e>
        <e type="operand">x</e>
        <e type="function" preserve="true" args="2">igamc</e>
      </input>
      <result action="numeric">
        <e type="operand">0.33</e>
      </result>
    </math>
  </region>
  <region id="49" left="0" top="1116" width="232" height="28" color="#000000" bgColor="#ffffff" fontSize="10">
    <math decimalPlaces="2">
      <input>
        <e type="operand">a</e>
        <e type="operand">a</e>
        <e type="operand">x</e>
        <e type="function" preserve="true" args="2">igamc</e>
        <e type="function" preserve="true" args="2">igami</e>
      </input>
      <result action="numeric">
        <e type="operand">3.14</e>
      </result>
    </math>
  </region>
  <region id="50" left="0" top="1152" width="211" height="26" color="#000000" bgColor="#ffffff" fontSize="10">
    <math decimalPlaces="2">
      <input>
        <e type="operand">a</e>
        <e type="operand">b</e>
        <e type="operand">0.1</e>
        <e type="operand">x</e>
        <e type="operator" args="2">*</e>
        <e type="function" preserve="true" args="3">ibeta</e>
      </input>
      <result action="numeric">
        <e type="operand">0.02</e>
      </result>
    </math>
  </region>
  <region id="51" left="252" top="1152" width="320" height="28" color="#000000" bgColor="#ffffff" fontSize="10">
    <math decimalPlaces="2">
      <input>
        <e type="operand">a</e>
        <e type="operand">b</e>
        <e type="operand">a</e>
        <e type="operand">b</e>
        <e type="operand">0.1</e>
        <e type="operand">x</e>
        <e type="operator" args="2">*</e>
        <e type="function" preserve="true" args="3">ibeta</e>
        <e type="function" preserve="true" args="3">ibetai</e>
      </input>
      <result action="numeric">
        <e type="operand">0.31</e>
      </result>
    </math>
  </region>
  <region id="52" left="0" top="1179" width="180" height="26" color="#000000" bgColor="#ffffff" fontSize="10">
    <math decimalPlaces="2">
      <input>
        <e type="operand">x</e>
        <e type="operand">k</e>
        <e type="function" preserve="true" args="2">binomial</e>
      </input>
      <result action="numeric">
        <e type="operand">1.28</e>
      </result>
    </math>
  </region>
  <region id="53" left="0" top="1224" width="446" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="rus">
      <p>6) Hypergeometric functions: 1F1, 2F0, 1F2, 2F1, 3F0.</p>
    </text>
  </region>
  <region id="54" left="0" top="1260" width="43" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <math decimalPlaces="2">
      <input>
        <e type="operand">a</e>
        <e type="operand">e</e>
        <e type="operator" args="2">:</e>
      </input>
    </math>
  </region>
  <region id="55" left="54" top="1260" width="76" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <math decimalPlaces="2">
      <input>
        <e type="operand">b</e>
        <e type="operand">1.265</e>
        <e type="operator" args="2">:</e>
      </input>
    </math>
  </region>
  <region id="56" left="135" top="1260" width="43" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <math decimalPlaces="2">
      <input>
        <e type="operand">c</e>
        <e type="operand">π</e>
        <e type="operator" args="2">:</e>
      </input>
    </math>
  </region>
  <region id="57" left="198" top="1260" width="60" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <math decimalPlaces="2">
      <input>
        <e type="operand">x</e>
        <e type="operand">0.5</e>
        <e type="operator" args="2">:</e>
      </input>
    </math>
  </region>
  <region id="58" left="0" top="1287" width="187" height="26" color="#000000" bgColor="#ffffff" fontSize="10">
    <math decimalPlaces="2">
      <input>
        <e type="operand">a</e>
        <e type="operand">b</e>
        <e type="operand">x</e>
        <e type="function" preserve="true" args="3">hyp1f1</e>
      </input>
      <result action="numeric">
        <e type="operand">2.64</e>
      </result>
    </math>
  </region>
  <region id="59" left="351" top="1287" width="187" height="26" color="#000000" bgColor="#ffffff" fontSize="10">
    <math decimalPlaces="2">
      <input>
        <e type="operand">a</e>
        <e type="operand">b</e>
        <e type="operand">x</e>
        <e type="function" preserve="true" args="3">hyp2f0</e>
      </input>
      <result action="numeric">
        <e type="operand">1.29</e>
      </result>
    </math>
  </region>
  <region id="60" left="0" top="1314" width="203" height="26" color="#000000" bgColor="#ffffff" fontSize="10">
    <math decimalPlaces="2">
      <input>
        <e type="operand">a</e>
        <e type="operand">b</e>
        <e type="operand">c</e>
        <e type="operand">x</e>
        <e type="function" preserve="true" args="4">hyp2f1</e>
      </input>
      <result action="numeric">
        <e type="operand">2.1</e>
      </result>
    </math>
  </region>
  <region id="61" left="351" top="1314" width="211" height="26" color="#000000" bgColor="#ffffff" fontSize="10">
    <math decimalPlaces="2">
      <input>
        <e type="operand">a</e>
        <e type="operand">b</e>
        <e type="operand">c</e>
        <e type="operand">x</e>
        <e type="function" preserve="true" args="4">hyp1f2</e>
      </input>
      <result action="numeric">
        <e type="operand">1.38</e>
      </result>
    </math>
  </region>
  <region id="62" left="0" top="1341" width="246" height="34" color="#000000" bgColor="#ffffff" fontSize="10">
    <math decimalPlaces="2">
      <input>
        <e type="operand">a</e>
        <e type="operand">b</e>
        <e type="operand">c</e>
        <e type="operand">x</e>
        <e type="function" preserve="true" args="4">hyp3f0</e>
      </input>
      <result action="numeric">
        <e type="operand">5.4</e>
        <e type="operand">10</e>
        <e type="operand">35</e>
        <e type="operator" args="2">^</e>
        <e type="operator" args="2">*</e>
      </result>
    </math>
  </region>
  <region id="63" left="0" top="1404" width="626" height="104" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="rus">
      <p>7) Elliptic Integrals: 
Legendre's canonical incomplete elliptic integral, Legendre's complete 
elliptic integral, associated Legendre's complete elliptic integral 
of the first, second and third kind; Jacobian elliptic functions 
cn(u,k), dn(u,k), sn(u,k) and their amplitude phi(u,k); 
Carlson's incomplete elliptic integral of the first, second and third kind.</p>
    </text>
  </region>
  <region id="64" left="0" top="1539" width="76" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <math decimalPlaces="2">
      <input>
        <e type="operand">x</e>
        <e type="operand">0.486</e>
        <e type="operator" args="2">:</e>
      </input>
    </math>
  </region>
  <region id="65" left="90" top="1539" width="68" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <math decimalPlaces="2">
      <input>
        <e type="operand">y</e>
        <e type="operand">0.86</e>
        <e type="operator" args="2">:</e>
      </input>
    </math>
  </region>
  <region id="66" left="180" top="1539" width="76" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <math decimalPlaces="2">
      <input>
        <e type="operand">k</e>
        <e type="operand">0.867</e>
        <e type="operator" args="2">:</e>
      </input>
    </math>
  </region>
  <region id="67" left="279" top="1539" width="117" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <math decimalPlaces="2">
      <input>
        <e type="operand">u</e>
        <e type="operand">0.52447529</e>
        <e type="operator" args="2">:</e>
      </input>
    </math>
  </region>
  <region id="68" left="0" top="1575" width="188" height="26" color="#000000" bgColor="#ffffff" fontSize="10">
    <math decimalPlaces="2">
      <input>
        <e type="operand">x</e>
        <e type="operand">k</e>
        <e type="function" preserve="true" args="2">LegendreF</e>
      </input>
      <result action="numeric">
        <e type="operand">0.52</e>
      </result>
    </math>
  </region>
  <region id="69" left="360" top="1575" width="172" height="26" color="#000000" bgColor="#ffffff" fontSize="10">
    <math decimalPlaces="2">
      <input>
        <e type="operand">k</e>
        <e type="function" preserve="true" args="1">LegendreKc</e>
      </input>
      <result action="numeric">
        <e type="operand">2.16</e>
      </result>
    </math>
  </region>
  <region id="70" left="0" top="1602" width="181" height="26" color="#000000" bgColor="#ffffff" fontSize="10">
    <math decimalPlaces="2">
      <input>
        <e type="operand">k</e>
        <e type="function" preserve="true" args="1">LegendreKc1</e>
      </input>
      <result action="numeric">
        <e type="operand">1.68</e>
      </result>
    </math>
  </region>
  <region id="71" left="0" top="1638" width="188" height="26" color="#000000" bgColor="#ffffff" fontSize="10">
    <math decimalPlaces="2">
      <input>
        <e type="operand">x</e>
        <e type="operand">k</e>
        <e type="function" preserve="true" args="2">LegendreE</e>
      </input>
      <result action="numeric">
        <e type="operand">0.49</e>
      </result>
    </math>
  </region>
  <region id="72" left="360" top="1638" width="172" height="26" color="#000000" bgColor="#ffffff" fontSize="10">
    <math decimalPlaces="2">
      <input>
        <e type="operand">k</e>
        <e type="function" preserve="true" args="1">LegendreEc</e>
      </input>
      <result action="numeric">
        <e type="operand">1.21</e>
      </result>
    </math>
  </region>
  <region id="73" left="0" top="1674" width="181" height="26" color="#000000" bgColor="#ffffff" fontSize="10">
    <math decimalPlaces="2">
      <input>
        <e type="operand">k</e>
        <e type="function" preserve="true" args="1">LegendreEc1</e>
      </input>
      <result action="numeric">
        <e type="operand">1.47</e>
      </result>
    </math>
  </region>
  <region id="74" left="0" top="1710" width="212" height="26" color="#000000" bgColor="#ffffff" fontSize="10">
    <math decimalPlaces="2">
      <input>
        <e type="operand">x</e>
        <e type="operand">y</e>
        <e type="operand">k</e>
        <e type="function" preserve="true" args="3">LegendreP</e>
      </input>
      <result action="numeric">
        <e type="operand">0.57</e>
      </result>
    </math>
  </region>
  <region id="75" left="360" top="1710" width="196" height="26" color="#000000" bgColor="#ffffff" fontSize="10">
    <math decimalPlaces="2">
      <input>
        <e type="operand">y</e>
        <e type="operand">k</e>
        <e type="function" preserve="true" args="2">LegendrePc</e>
      </input>
      <result action="numeric">
        <e type="operand">6.78</e>
      </result>
    </math>
  </region>
  <region id="76" left="0" top="1746" width="205" height="26" color="#000000" bgColor="#ffffff" fontSize="10">
    <math decimalPlaces="2">
      <input>
        <e type="operand">y</e>
        <e type="operand">k</e>
        <e type="function" preserve="true" args="2">LegendrePc1</e>
      </input>
      <result action="numeric">
        <e type="operand">4.65</e>
      </result>
    </math>
  </region>
  <region id="77" left="0" top="1782" width="130" height="26" color="#000000" bgColor="#ffffff" fontSize="10">
    <math decimalPlaces="2">
      <input>
        <e type="operand">u</e>
        <e type="operand">k</e>
        <e type="function" preserve="true" args="2">cn</e>
      </input>
      <result action="numeric">
        <e type="operand">0.87</e>
      </result>
    </math>
  </region>
  <region id="78" left="207" top="1782" width="130" height="26" color="#000000" bgColor="#ffffff" fontSize="10">
    <math decimalPlaces="2">
      <input>
        <e type="operand">u</e>
        <e type="operand">k</e>
        <e type="function" preserve="true" args="2">dn</e>
      </input>
      <result action="numeric">
        <e type="operand">0.91</e>
      </result>
    </math>
  </region>
  <region id="79" left="405" top="1782" width="130" height="26" color="#000000" bgColor="#ffffff" fontSize="10">
    <math decimalPlaces="2">
      <input>
        <e type="operand">u</e>
        <e type="operand">k</e>
        <e type="function" preserve="true" args="2">sn</e>
      </input>
      <result action="numeric">
        <e type="operand">0.49</e>
      </result>
    </math>
  </region>
  <region id="80" left="0" top="1818" width="139" height="26" color="#000000" bgColor="#ffffff" fontSize="10">
    <math decimalPlaces="2">
      <input>
        <e type="operand">u</e>
        <e type="operand">k</e>
        <e type="function" preserve="true" args="2">phi</e>
      </input>
      <result action="numeric">
        <e type="operand">0.51</e>
      </result>
    </math>
  </region>
  <region id="81" left="0" top="1854" width="154" height="26" color="#000000" bgColor="#ffffff" fontSize="10">
    <math decimalPlaces="2">
      <input>
        <e type="operand">x</e>
        <e type="operand">y</e>
        <e type="operand">k</e>
        <e type="function" preserve="true" args="3">Rf</e>
      </input>
      <result action="numeric">
        <e type="operand">1.18</e>
      </result>
    </math>
  </region>
  <region id="82" left="207" top="1854" width="154" height="26" color="#000000" bgColor="#ffffff" fontSize="10">
    <math decimalPlaces="2">
      <input>
        <e type="operand">x</e>
        <e type="operand">y</e>
        <e type="operand">k</e>
        <e type="function" preserve="true" args="3">Rd</e>
      </input>
      <result action="numeric">
        <e type="operand">1.46</e>
      </result>
    </math>
  </region>
  <region id="83" left="405" top="1854" width="178" height="26" color="#000000" bgColor="#ffffff" fontSize="10">
    <math decimalPlaces="2">
      <input>
        <e type="operand">x</e>
        <e type="operand">y</e>
        <e type="operand">k</e>
        <e type="operand">u</e>
        <e type="function" preserve="true" args="4">Rj</e>
      </input>
      <result action="numeric">
        <e type="operand">1.97</e>
      </result>
    </math>
  </region>
  <region id="84" left="0" top="1899" width="632" height="40" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="rus">
      <p>8) Dawson's integral, Fresnel integrals, dilogarithm, Riemann zeta function 
and Riemann zeta function of two arguments.</p>
    </text>
  </region>
  <region id="85" left="0" top="1953" width="43" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <math decimalPlaces="2">
      <input>
        <e type="operand">x</e>
        <e type="operand">e</e>
        <e type="operator" args="2">:</e>
      </input>
    </math>
  </region>
  <region id="86" left="0" top="1980" width="131" height="26" color="#000000" bgColor="#ffffff" fontSize="10">
    <math decimalPlaces="2">
      <input>
        <e type="operand">x</e>
        <e type="function" preserve="true" args="1">Dawson</e>
      </input>
      <result action="numeric">
        <e type="operand">0.2</e>
      </result>
    </math>
  </region>
  <region id="87" left="207" top="1980" width="148" height="26" color="#000000" bgColor="#ffffff" fontSize="10">
    <math decimalPlaces="2">
      <input>
        <e type="operand">x</e>
        <e type="function" preserve="true" args="1">FresnelC</e>
      </input>
      <result action="numeric">
        <e type="operand">0.4</e>
      </result>
    </math>
  </region>
  <region id="88" left="414" top="1980" width="156" height="26" color="#000000" bgColor="#ffffff" fontSize="10">
    <math decimalPlaces="2">
      <input>
        <e type="operand">x</e>
        <e type="function" preserve="true" args="1">FresnelS</e>
      </input>
      <result action="numeric">
        <e type="operand">0.44</e>
      </result>
    </math>
  </region>
  <region id="89" left="0" top="2007" width="140" height="26" color="#000000" bgColor="#ffffff" fontSize="10">
    <math decimalPlaces="2">
      <input>
        <e type="operand">x</e>
        <e type="function" preserve="true" args="1">dilog</e>
      </input>
      <result action="numeric">
        <e type="operand">1.28</e>
        <e type="operator" args="1">-</e>
      </result>
    </math>
  </region>
  <region id="90" left="207" top="2007" width="123" height="26" color="#000000" bgColor="#ffffff" fontSize="10">
    <math decimalPlaces="2">
      <input>
        <e type="operand">x</e>
        <e type="function" preserve="true" args="1">Zeta</e>
      </input>
      <result action="numeric">
        <e type="operand">1.27</e>
      </result>
    </math>
  </region>
  <region id="91" left="414" top="2007" width="176" height="26" color="#000000" bgColor="#ffffff" fontSize="10">
    <math decimalPlaces="2">
      <input>
        <e type="operand">x</e>
        <e type="operand">x</e>
        <e type="operand">1</e>
        <e type="operator" args="2">+</e>
        <e type="function" preserve="true" args="2">Zeta2</e>
      </input>
      <result action="numeric">
        <e type="operand">0.08</e>
      </result>
    </math>
  </region>
  <region id="92" left="0" top="2052" width="451" height="40" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="rus">
      <p>9) Exponential integral Ei, sine and cosine integrals 
and hyperbolic sine and cosine integrals.</p>
    </text>
  </region>
  <region id="93" left="0" top="2097" width="43" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <math decimalPlaces="2">
      <input>
        <e type="operand">n</e>
        <e type="operand">5</e>
        <e type="operator" args="2">:</e>
      </input>
    </math>
  </region>
  <region id="94" left="63" top="2097" width="43" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <math decimalPlaces="2">
      <input>
        <e type="operand">x</e>
        <e type="operand">π</e>
        <e type="operator" args="2">:</e>
      </input>
    </math>
  </region>
  <region id="95" left="0" top="2124" width="130" height="26" color="#000000" bgColor="#ffffff" fontSize="10">
    <math decimalPlaces="2">
      <input>
        <e type="operand">n</e>
        <e type="operand">x</e>
        <e type="function" preserve="true" args="2">Ei</e>
      </input>
      <result action="numeric">
        <e type="operand">0.01</e>
      </result>
    </math>
  </region>
  <region id="96" left="0" top="2151" width="106" height="26" color="#000000" bgColor="#ffffff" fontSize="10">
    <math decimalPlaces="2">
      <input>
        <e type="operand">x</e>
        <e type="function" preserve="true" args="1">Si</e>
      </input>
      <result action="numeric">
        <e type="operand">1.85</e>
      </result>
    </math>
  </region>
  <region id="97" left="369" top="2151" width="106" height="26" color="#000000" bgColor="#ffffff" fontSize="10">
    <math decimalPlaces="2">
      <input>
        <e type="operand">x</e>
        <e type="function" preserve="true" args="1">Ci</e>
      </input>
      <result action="numeric">
        <e type="operand">0.07</e>
      </result>
    </math>
  </region>
  <region id="98" left="0" top="2187" width="115" height="26" color="#000000" bgColor="#ffffff" fontSize="10">
    <math decimalPlaces="2">
      <input>
        <e type="operand">x</e>
        <e type="function" preserve="true" args="1">Shi</e>
      </input>
      <result action="numeric">
        <e type="operand">5.47</e>
      </result>
    </math>
  </region>
  <region id="99" left="369" top="2187" width="115" height="26" color="#000000" bgColor="#ffffff" fontSize="10">
    <math decimalPlaces="2">
      <input>
        <e type="operand">x</e>
        <e type="function" preserve="true" args="1">Chi</e>
      </input>
      <result action="numeric">
        <e type="operand">5.46</e>
      </result>
    </math>
  </region>
  <region id="100" left="0" top="2232" width="664" height="56" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="rus">
      <p>10) Legendre polynomials and associated functions of the first and second kind; 
normalised Legendre polynomials and associated functions of the first kind, 
spherical harmonics and sequences of spherical harmonics.</p>
    </text>
  </region>
  <region id="101" left="0" top="2313" width="68" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <math decimalPlaces="2">
      <input>
        <e type="operand">n</e>
        <e type="operand">3.59</e>
        <e type="operator" args="2">:</e>
      </input>
    </math>
  </region>
  <region id="102" left="90" top="2313" width="43" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <math decimalPlaces="2">
      <input>
        <e type="operand">m</e>
        <e type="operand">3</e>
        <e type="operator" args="2">:</e>
      </input>
    </math>
  </region>
  <region id="103" left="153" top="2313" width="117" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <math decimalPlaces="2">
      <input>
        <e type="operand">x</e>
        <e type="operand">0.12488512</e>
        <e type="operator" args="2">:</e>
      </input>
    </math>
  </region>
  <region id="104" left="270" top="2313" width="43" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <math decimalPlaces="2">
      <input>
        <e type="operand">l</e>
        <e type="operand">4</e>
        <e type="operator" args="2">:</e>
      </input>
    </math>
  </region>
  <region id="105" left="333" top="2313" width="52" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <math decimalPlaces="2">
      <input>
        <e type="operand">k</e>
        <e type="operand">2</e>
        <e type="operator" args="1">-</e>
        <e type="operator" args="2">:</e>
      </input>
    </math>
  </region>
  <region id="106" left="396" top="2313" width="91" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <math decimalPlaces="2">
      <input>
        <e type="operand">θ</e>
        <e type="operand">0.577</e>
        <e type="operand">π</e>
        <e type="operator" args="2">*</e>
        <e type="operator" args="2">:</e>
      </input>
    </math>
  </region>
  <region id="107" left="549" top="2313" width="83" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <math decimalPlaces="2">
      <input>
        <e type="operand">ϕ</e>
        <e type="operand">1.56</e>
        <e type="operand">π</e>
        <e type="operator" args="2">*</e>
        <e type="operator" args="2">:</e>
      </input>
    </math>
  </region>
  <region id="108" left="0" top="2349" width="180" height="26" color="#000000" bgColor="#ffffff" fontSize="10">
    <math decimalPlaces="2">
      <input>
        <e type="operand">n</e>
        <e type="operand">m</e>
        <e type="operand">x</e>
        <e type="function" preserve="true" args="3">Plm</e>
      </input>
      <result action="numeric">
        <e type="operand">19.94</e>
        <e type="operator" args="1">-</e>
      </result>
    </math>
  </region>
  <region id="109" left="252" top="2349" width="171" height="26" color="#000000" bgColor="#ffffff" fontSize="10">
    <math decimalPlaces="2">
      <input>
        <e type="operand">n</e>
        <e type="operand">m</e>
        <e type="operand">x</e>
        <e type="function" preserve="true" args="3">Qlm</e>
      </input>
      <result action="numeric">
        <e type="operand">19.86</e>
      </result>
    </math>
  </region>
  <region id="110" left="0" top="2376" width="172" height="26" color="#000000" bgColor="#ffffff" fontSize="10">
    <math decimalPlaces="2">
      <input>
        <e type="operand">l</e>
        <e type="operand">k</e>
        <e type="operand">x</e>
        <e type="function" preserve="true" args="3">plm</e>
      </input>
      <result action="numeric">
        <e type="operand">0.74</e>
        <e type="operator" args="1">-</e>
      </result>
    </math>
  </region>
  <region id="111" left="252" top="2376" width="248" height="26" color="#000000" bgColor="#ffffff" fontSize="10">
    <math decimalPlaces="2">
      <input>
        <e type="operand">l</e>
        <e type="operand">k</e>
        <e type="operand">θ</e>
        <e type="operand">ϕ</e>
        <e type="function" preserve="true" args="4">Ylm</e>
      </input>
      <result action="numeric">
        <e type="operand">0.18</e>
        <e type="operand">0.07</e>
        <e type="operand">i</e>
        <e type="operator" args="2">*</e>
        <e type="operator" args="2">-</e>
      </result>
    </math>
  </region>
  <region id="112" left="0" top="2412" width="233" height="98" color="#000000" bgColor="#ffffff" fontSize="10">
    <math decimalPlaces="2">
      <input>
        <e type="operand">l</e>
        <e type="operand">θ</e>
        <e type="operand">ϕ</e>
        <e type="function" preserve="true" args="3">Yl</e>
      </input>
      <result action="numeric">
        <e type="operand">0.15</e>
        <e type="operand">0.05</e>
        <e type="operator" args="1">-</e>
        <e type="operand">0.28</e>
        <e type="operand">i</e>
        <e type="operator" args="2">*</e>
        <e type="operator" args="2">+</e>
        <e type="operand">0.18</e>
        <e type="operand">0.07</e>
        <e type="operand">i</e>
        <e type="operator" args="2">*</e>
        <e type="operator" args="2">+</e>
        <e type="operand">0.15</e>
        <e type="operator" args="1">-</e>
        <e type="operand">0.23</e>
        <e type="operand">i</e>
        <e type="operator" args="2">*</e>
        <e type="operator" args="2">+</e>
        <e type="operand">0.29</e>
        <e type="operand">0.27</e>
        <e type="operand">i</e>
        <e type="operator" args="2">*</e>
        <e type="operator" args="2">+</e>
        <e type="operand">5</e>
        <e type="operand">1</e>
        <e type="function" preserve="true" args="7">mat</e>
      </result>
    </math>
  </region>
  <region id="113" left="0" top="2538" width="630" height="40" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="rus">
      <p>11) Simple and useful functions: round x to nearest or even integer number, 
sign of x and complex sign of x, semifactorial.</p>
    </text>
  </region>
  <region id="114" left="0" top="2592" width="52" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <math decimalPlaces="2">
      <input>
        <e type="operand">x</e>
        <e type="operand">π</e>
        <e type="operator" args="1">-</e>
        <e type="operator" args="2">:</e>
      </input>
    </math>
  </region>
  <region id="115" left="72" top="2592" width="58" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <math decimalPlaces="2">
      <input>
        <e type="operand">z</e>
        <e type="operand">i</e>
        <e type="operand">π</e>
        <e type="operator" args="2">*</e>
        <e type="operator" args="2">:</e>
      </input>
    </math>
  </region>
  <region id="116" left="351" top="2610" width="182" height="34" color="#000000" bgColor="#ffffff" fontSize="10">
    <math decimalPlaces="2">
      <input>
        <e type="operand">21</e>
        <e type="function" preserve="true" args="1">sfact</e>
      </input>
      <result action="numeric">
        <e type="operand">1.37</e>
        <e type="operand">10</e>
        <e type="operand">10</e>
        <e type="operator" args="2">^</e>
        <e type="operator" args="2">*</e>
      </result>
    </math>
  </region>
  <region id="117" left="0" top="2619" width="115" height="26" color="#000000" bgColor="#ffffff" fontSize="10">
    <math decimalPlaces="2">
      <input>
        <e type="operand">x</e>
        <e type="function" preserve="true" args="1">round</e>
      </input>
      <result action="numeric">
        <e type="operand">3</e>
        <e type="operator" args="1">-</e>
      </result>
    </math>
  </region>
  <region id="118" left="126" top="2619" width="123" height="26" color="#000000" bgColor="#ffffff" fontSize="10">
    <math decimalPlaces="2">
      <input>
        <e type="operand">x</e>
        <e type="function" preserve="true" args="1">signum</e>
      </input>
      <result action="numeric">
        <e type="operand">1</e>
        <e type="operator" args="1">-</e>
      </result>
    </math>
  </region>
  <region id="119" left="252" top="2619" width="98" height="26" color="#000000" bgColor="#ffffff" fontSize="10">
    <math decimalPlaces="2">
      <input>
        <e type="operand">z</e>
        <e type="function" preserve="true" args="1">csgn</e>
      </input>
      <result action="numeric">
        <e type="operand">1</e>
      </result>
    </math>
  </region>
  <region id="120" left="0" top="2655" width="633" height="88" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="rus">
      <p>Note: there is a bug in the MathCad routine for the computation 
of modified Bessel functions of first kind In for n&gt;1 and large values 
of x (i.e. x&gt;50); below MathCad's In and Kn are checked against Iv and Kv 
and the Wronskian W(n,x)=In(n,x)Kn(n+1,x)+In(n+1,x)Kn(n,x), which satisfies 
the condition z*W(n,z)=1, is computed with both couples of functions.</p>
    </text>
  </region>
  <region id="121" left="9" top="2772" width="43" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <math decimalPlaces="2">
      <input>
        <e type="operand">n</e>
        <e type="operand">3</e>
        <e type="operator" args="2">:</e>
      </input>
    </math>
  </region>
  <region id="122" left="72" top="2772" width="60" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <math decimalPlaces="2">
      <input>
        <e type="operand">x</e>
        <e type="operand">600</e>
        <e type="operator" args="2">:</e>
      </input>
    </math>
  </region>
  <region id="123" left="0" top="2808" width="194" height="49" color="#000000" bgColor="#ffffff" fontSize="10">
    <math error="42" decimalPlaces="2">
      <input>
        <e type="operand">n</e>
        <e type="operand">x</e>
        <e type="function" args="2">Kn</e>
        <e type="operand">n</e>
        <e type="operand">x</e>
        <e type="function" preserve="true" args="2">Kv</e>
        <e type="operator" args="2">-</e>
        <e type="function" preserve="true" args="1">abs</e>
        <e type="operand">n</e>
        <e type="operand">x</e>
        <e type="function" args="2">Kn</e>
        <e type="function" preserve="true" args="1">abs</e>
        <e type="operand">n</e>
        <e type="operand">x</e>
        <e type="function" preserve="true" args="2">Kv</e>
        <e type="function" preserve="true" args="1">abs</e>
        <e type="operator" args="2">+</e>
        <e type="operator" args="2">/</e>
      </input>
      <result action="numeric">
        <e type="operand">#</e>
      </result>
    </math>
  </region>
  <region id="124" left="333" top="2808" width="194" height="49" color="#000000" bgColor="#ffffff" fontSize="10">
    <math error="42" decimalPlaces="2">
      <input>
        <e type="operand">n</e>
        <e type="operand">x</e>
        <e type="function" args="2">In</e>
        <e type="operand">n</e>
        <e type="operand">x</e>
        <e type="function" preserve="true" args="2">Iv</e>
        <e type="operator" args="2">-</e>
        <e type="function" preserve="true" args="1">abs</e>
        <e type="operand">n</e>
        <e type="operand">x</e>
        <e type="function" args="2">In</e>
        <e type="function" preserve="true" args="1">abs</e>
        <e type="operand">n</e>
        <e type="operand">x</e>
        <e type="function" preserve="true" args="2">Iv</e>
        <e type="function" preserve="true" args="1">abs</e>
        <e type="operator" args="2">+</e>
        <e type="operator" args="2">/</e>
      </input>
      <result action="numeric">
        <e type="operand">#</e>
      </result>
    </math>
  </region>
  <region id="125" left="0" top="2880" width="377" height="28" color="#000000" bgColor="#ffffff" fontSize="10">
    <math error="42" decimalPlaces="2">
      <input>
        <e type="operand">n</e>
        <e type="operand">x</e>
        <e type="function" args="2">In</e>
        <e type="operand">n</e>
        <e type="operand">1</e>
        <e type="operator" args="2">+</e>
        <e type="operand">x</e>
        <e type="function" args="2">Kn</e>
        <e type="operator" args="2">*</e>
        <e type="operand">n</e>
        <e type="operand">x</e>
        <e type="function" args="2">Kn</e>
        <e type="operand">n</e>
        <e type="operand">1</e>
        <e type="operator" args="2">+</e>
        <e type="operand">x</e>
        <e type="function" args="2">In</e>
        <e type="operator" args="2">*</e>
        <e type="operator" args="2">+</e>
        <e type="bracket">(</e>
        <e type="operand">x</e>
        <e type="operator" args="2">*</e>
      </input>
      <result action="numeric">
        <e type="operand">#</e>
      </result>
    </math>
  </region>
  <region id="126" left="0" top="2916" width="377" height="28" color="#000000" bgColor="#ffffff" fontSize="10">
    <math decimalPlaces="2">
      <input>
        <e type="operand">n</e>
        <e type="operand">x</e>
        <e type="function" preserve="true" args="2">Iv</e>
        <e type="operand">n</e>
        <e type="operand">1</e>
        <e type="operator" args="2">+</e>
        <e type="operand">x</e>
        <e type="function" preserve="true" args="2">Kv</e>
        <e type="operator" args="2">*</e>
        <e type="operand">n</e>
        <e type="operand">x</e>
        <e type="function" preserve="true" args="2">Kv</e>
        <e type="operand">n</e>
        <e type="operand">1</e>
        <e type="operator" args="2">+</e>
        <e type="operand">x</e>
        <e type="function" preserve="true" args="2">Iv</e>
        <e type="operator" args="2">*</e>
        <e type="operator" args="2">+</e>
        <e type="bracket">(</e>
        <e type="operand">x</e>
        <e type="operator" args="2">*</e>
      </input>
      <result action="numeric">
        <e type="operand">0</e>
      </result>
    </math>
  </region>
  <region id="127" left="0" top="2952" width="664" height="600" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="eng">
      <p>This MathCad file contains usage documentation for the functions provided
with the library. It is free software; the only restrictions are those 
coming from the owners of the numerical codes used. It is written in C 
but part of the codes were originally in fortan.

Most of the code for the numerical computation of special functions 
have been taken from the Cephes Math Library Copyrighted by Stephen L. Moshier. 
Other codes come from the Collected Algorithms (CALGO) by ACM and SLATEC,
which are available from netlib; these includes:

1) file 644 by D.E. Amos for the computation of scaled and unscaled Bessel
and Airy functions of complex argument;

2) file 577 by B.C. Carlson and E.M. Notis for symmetric incomplete 
elliptic integrals of the first, second, and third kind which are also 
used to compute LegendreP;

3) dxlegf and associated routines from slatec, by J. M. Smith for 
Legendre polynomials and associated functions;

4) a modification of the (fortran single precision) code given in file 404 
for the computation of complex logarithmic gamma function (use with care).

Moreover an alternative implementation of the algorithm for Psi (digamma) 
function distributed with Mathcad 7.0 Pro is provided. The conversion from 
fortran has been performed with f2c for 644, 577 and dxlegf, while 404 was 
completely rewritten in C, using some Cephes function for complex numbers
which are always intended in the cut plane -pi &lt; arg(z) &lt;= pi.

Please send comments, suggestions and bug reports atthe email address 
gborzi@dees.unict.it . If you have C or fortran codes for the computation 
of further special functions or other numerical software in C or fortran 
and you wantto include it in the library you can send me your source codes; 
remember that non free software will not be included in the library.

An homepage for the library is available at 
http://wwwelfin.dees.unict.it/esg/mathlib.htm.</p>
    </text>
  </region>
  <region id="128" left="0" top="3564" width="647" height="152" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="rus">
      <p>Acknowledgments.
I wish to thank Professors S. L. Moshier and the ACM for having provided 
the numerical software used to build the library.

Giuseppe Borzi' - Ph.D. student at the Electrical and Electronical Department 
of the University of Catania - Italia.

gborzi@dees.unict.it
http://wwwelfin.dees.unict.it/esg/gborzi.html</p>
    </text>
  </region>
</regions>