2f367764-94da-4fb1-9c2a-7ac1697b886b 19 overlord 4 5 false false 1 decimal

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

Applications overlord ... Γ(x)

Gamma Function ##_p 57.156235665862923517 59.597960355475491248 - 14.136097974741747174 0.49191381609762019978 - 0.33994649984811888699 104 -^* 0.46523628927048575665 104 -^* 0.98374475304879564677 - (104 -^* 0.15808870322491248884 103 -^* 0.21026444172410488319 - (103 -^* 0.21743961811521264320 103 -^* 0.16431810653676389022 - (103 -^* 0.84418223983852743293 104 -^* 0.26190838401581408670 - (104 -^* 0.36899182659531622704 105 -^* 72 mat : a Γ ∞ a 0 ≤ (a a trunc ≡ (& a 1 - (! a a trunc ≡ ##a.T a - a 0.5 < a 1 - cases : ##x 0.99999999999999709182 : ##g 4.7421875 : ##i 1 ##_p length range ##x ##x ##_p ##i el ##a.T ##i + / + eval : for ##t ##a.T ##g + 0.5 + eval : ##S ##t ##a.T 0.5 + 1.25 /^e ##t -^2 π * sqrt * ##x * (1 1.25 /^* (1.25^: π π a * sin ##S * / a 0.5 < ##S cases 71 line cases 11 line : 21 line

Lower Incomplete Gamma Function a x γ x a^e x -^* x k^a j + (j 0 k product / k 050 sum * 11 line :

Upper Incomplete Gamma Function a x Γ a Γ a x γ - 11 line :

Example_1: Multistage XFR

t.0 0 time :

System TimeConstant T 1 :

Laplace UnitStep s 1 :

x λ 10 x ≤ (x 20 ≤ (& cases :

time 7 :

Laplace XFR multistage system'n' stages, 'T' time constant n t f n 1 + Γ n 1 + t T / Γ - s n 1 + Γ * / 11 line :

3 x f x λ * 6 x f x λ * 9 x f x λ * time 1.25 time 0.25 - 2 2 mat 6 1 sys

3 time f 6 time f 9 time f 31 mat 0.9182 0.5503 0.1695 31 mat

Example_2: Fitting a data set.

XY 0 127.42 0.1 123.469 0.2 118.008 0.3 111.187 0.4 102.811 0.5 93.554 0.6 84.168 0.7 74.818 0.8 66.373 0.9 58.587 1 51.678 1.1 45.739 1.2 40.675 1.3 36.404 1.4 32.74 1.5 29.581 1.6 26.848 1.7 24.472 1.8 22.395 1.9 20.573 2 18.97 2.1 17.555 2.2 16.3 2.3 15.184 2.4 14.188 2.5 13.295 2.6 12.492 2.7 11.768 2.8 11.12 2.9 10.547 3 10.028 312 mat :

Fitting a data set Γ(a,x) ... data Mathsoft

data char size clr plot k 1 data rows range r3 k el char : r4 k el size : r5 k el clr : 13 mat for data r3 r4 r5 augment 21 line :

pts XY o 5 black plot :

ε 103 -^:

yo 10.028 : a 143.017 : b 1.7666 : n 2.486 : 14 mat

x f yo a b x Γ (n^* + :

Ω u u f vectorize augment :

u ε 3 0.05 range :

pts Ω 2 1 sys

yo 10.028 : a 143.01681 : b 1.766652 : n 2.48644 : 14 mat

0 time t.0 - ms 6658

5 - Γ ∞

1.65 - Γ 2.37402981558256

0.928153 Γ 1.04694145892327

6 Γ 120

17.23 Γ 39934563646512.6

171.6243 Γ 1.79698185749562 10308^*

x Γ 6 - x 0.1 10 solve 0.155233499506802 3.99999998160025 21 mat

x Γ 7.4756 - x 0.1 ≡ 103 -^1013 -^FindRoot 0.125929664570172