384cf127-1349-4426-a57d-c46f9348bd4b 300 overlord 4 5 false false 1 decimal

&[DATE] &[TIME]

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 #S ∞ : #a 0 ≤ (#a #a trunc ≡ (& #S #a 1 - (! : #a #a trunc ≡ #a.T #a - #a 0.5 < #a 1 - cases : #fct 1.5 #a 165 - < (#a 165 > (| 0 cases : 21 line cases #img 0 : 21 line #a Im 0 ≡ #a.T #a 1 - : #fct 0 : #img 1 : 31 line cases #S #S IsDefined #x 0.99999999999999709182 #_p #i el #a.T #i + / #i 114 sum + : #g 4.7421875 : #a.T #a.T 0.5 + : #S #a.T #g + e / (#a.T^e #g -^2 π * sqrt * #x * (* : #fct 0 ≡ #S #a.T #g + e / (#a.T #fct /^e #g -^2 π * sqrt * #x * (1 #fct /^* (#fct^: cases π π #a * sin #S * / #a 0.5 < (#S cases #img 1 < #S cases 51 line cases 21 line : 21 line

Lower Incomplete Gamma Function ##a ##x γ #SS 0 : #k 070 range #TT 1 : #j 0 #k range #TT #TT ##a #j + (* : for #SS #SS ##x #k^#TT / + : 31 line for #SS ##x ##a^* e ##x -^* 31 line :

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

10 - Γ ∞

x Γ

4.2 - Γ 0.164061050477615 -

0.3 - Γ 4.32685110882521 -

0 Γ ∞

0.1 Γ 9.51350769866877

0.928153 Γ 1.04694145892326

π Γ 2.28803779534001

6 Γ 120

12.45 Γ 120865870.522176

23.5 Γ 5.36130358754441 1021^*

65.494 Γ 9.95774536800841 1089^*

171.62 Γ 1.75768267899778 10308^*

3 - 2 i * + Γ 0.001702084799023 - 0.002895711899941 i * -

2.5 i * Γ 0.016129054047794 0.026749108945949 i * -

x Γ 8.4563 - x 0.1 10 solve 0.111927057310304 4.2654172807227 21 mat

x Γ 8.4563 - 0.11 FindRoot 0.1119

a 0.5 :

x Γ 8.4563 - 4 FindRoot 4.2654

x λ 10 x ≤ (x 2 a * ≤ (& cases :

x 3 γ 4.7239 - x 0.1 10 solve 0.194015731882421 5.08035946033243 21 mat

Jnct a a Γ a a γ + 2 / :

x 3 Γ 5.0803 - x 0.1 10 solve 4.1705

X 0.1 a 0.11 range : i 1 X rows range Y i el a X i el Γ : for x f X Y x cinterp : 31 line

x equ x 3 γ 4.7239 - :

v r v 1 el equ :

0.15 11 mat 01010 -^x r al_nleqsolve 0.19401492536895 11 mat

511 mat 01010 -^x r al_nleqsolve 5.08035947893513 11 mat

U x f Jnct - 0 ≡ x X 1 el a solve :

a x Γ x λ * a x γ x λ * U a U Γ + 50 black 1 5 mat a a a Γ . 14 blue 1 5 mat a a a γ . 14 red 1 5 mat 5 1 sys

j 0 :

t.0 0 time :

i 130 1.01 range j j 1 + : cc j el i Γ : 21 line for

0 time t.0 - 2.034 s *

j 2901