f0892fe5-9d47-42fd-8ec6-4673666506c8 18 4 5 decimal

&[DATE] &[TIME] - &[FILENAME]

http://www.jekyll.math.byuh.edu/courses/m321/handouts/gammaproperties.pdf

http://mhtlab.uwaterloo.ca/courses/me755/web_chap1.pdf

0

η 1.46163214496836 : (minΓ(x)=> 0.885603194410895 ≡

x 4.5 1 - ^ x - exp * x 0.5 1 - ^ x - exp * x η 1 - ^ x - exp * 3 1 sys

Sanity => 11.6317283965675 x 4.5 1 -^x - exp * x 0100 int 11.6317283965661

Sanity => sqrt(π)= 1.77245385090551
Mathcad TOL 10e-11 => 1.77245385090555
Smath fails: "x_not defined" .../0 x 0.5 1 -^x - exp * x 0100 int #

Sanity => 0.885603194410895 x η 1 -^x - exp * x 0100 int 0.88554

Exact x 3^x 0 π int 24.3522727585006

Abramowitz & Stegun, p. 256 c 1 0.5772156649015329 0.6558780715202538 - 0.0420026350340952 - 0.1665386113822915 0.0421977345555443 - 0.0096219715278770 - 0.0072189432466630 0.0011651675918591 - 0.0002152416741149 - 0.0001280502823882 0.0000201348547807 - 0.0000012504934821 - 0.0000011330272320 0.0000002056338417 - 0.0000000061160950 0.0000000050020075 0.0000000011812746 - 0.0000000001043427 0.0000000000077823 0.0000000000036968 - 0.0000000000005100 0.0000000000000206 - 0.0000000000000054 - 0.0000000000000014 0.0000000000000001 261 mat :

1 z Γ / c k el z k^* k 1 ∞ sum ≡

z Γpoly c k el z k^* k 126 sum :

0.5 Γpoly 0.564189583547756

1 0.5 Γpoly / π sqrt 1 π Γpoly / 11 Γpoly / 1 0.1 Γpoly / 1 1.461632144968362 Γpoly / 61 mat 1.77245385090552 1.77245385090551 2.27683637061996 1 9.51350769866873 0.885603194406434 61 mat

1.461632144968362 0.885603194410889 12 mat

x Γ 1 x Γpoly / 0 x ≤ (x 1 ≤ (& inaccurate cases :

1.23456789 Γ 0.123456789 Γ 21 mat inaccurate 7.63270318879871 21 mat

x Γ 1 x Γpoly / :

x c 10 x ≤ (x 1 ≤ (& cases :

result for Γ(2.5) z 1.5 :

z 1 + Γ z z Γ * ≡

x Γpoly x c * x Γ x c * 2 1 sys

10½  Decimals z Γ z * 1.32934038817

x Γpoly x c *