2f367764-94da-4fb1-9c2a-7ac1697b886b 26 overlord 4 5 decimal

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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 : x Γ ∞ x 0 ≤ (x x trunc ≡ (& x 1 - (! x x trunc ≡ U x - x 0.5 ≤ x 1 - cases : u 0.99999999999999709182 : g 4.7421875 : i 1 p length range u u p i el U i + / + eval : for t U g + 0.5 + eval : S t U 0.5 + 1.25 /^t - exp 2 π * sqrt * u * (1 1.25 /^* (1.25^: π π x * sin S * / x 0.5 ≤ S cases 71 line cases 11 line : 21 line

Lower Incomplete Gamma Function a x γ x a^x - exp * 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 :

1 0.123456789 Γ 0.883859832886162

ε 1017 -^:

ε solves Uncertainty 1 ε Γ 1.000000000000000

Example_1: Multistage XFR

t0 0 time :

System TimeConstant T 1 :

Laplace UnitStep s 1 :

time 7 :

x λ 10 x ≤ (x 20 ≤ (& cases :

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 0.918 0.55 0.17 31 mat

Example_2: Fitting Mathsoft 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 :

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 : b 1.77 : n 2.5 : 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 t0 - 19.6 s *

5 - Γ ∞

1.65 - Γ 2.37402981558258

0.987654321 Γ 1.00727859773676

6 Γ 120

17.23 Γ 39934563646510.3

165 Γ 3.287218585534300 10293^*

X x Γ 6 - 0 ≡ x 05 solve : 0.155233596001376 421 mat

X Γ vectorize 5.999535 621 mat

Example_3:incertitude sur N mesures ayant σ

N 12 :

σ 0.75 :

2 N 1 - / sqrt N 2 / Γ N 1 - 2 / Γ / * σ * 0.7332

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Ucertainty on vector of μ & σ

vy 25.527 25.51 25.512 25.511 25.511 25.508 25.487 25.501 81 mat :

vy incertitude n vy length : u vy StdDev n sqrt / n 1 - 2 / Γ n 1 - sqrt * n 2 / Γ 2 sqrt * / * : 21 line :

MCD 0.00418 vy incertitude 0.00413

vy vy 0.00413 ± ≡