Data commit

Task/Gamma-function/Lambdatalk/gamma-function.lambdatalk

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+{def gamma.p
+ {A.new 0.99999999999980993
+      676.5203681218851
+    -1259.1392167224028
+      771.32342877765313
+     -176.61502916214059
+       12.507343278686905
+       -0.13857109526572012
+        9.9843695780195716e-6
+        1.5056327351493116e-7
+}}
+-> gamma.p
+
+{def gamma.rec
+ {lambda {:x :a :i}
+  {if {< :i {A.length {gamma.p}}}
+   then {gamma.rec :x
+                   {+ :a {/ {A.get :i {gamma.p}} {+ :x :i}} }
+                   {+ :i 1}}
+   else :a
+}}}
+-> gamma.rec
+
+{def gamma
+ {lambda {:x}
+  {if {< :x 0.5}
+   then {/ {PI}
+           {* {sin {* {PI} :x}}
+              {gamma {- 1 :x}}}}
+   else {let { {:x {- :x 1}}
+               {:t {+ {- :x 1} 7 0.5}}
+             } {* {sqrt {* 2 {PI}}}
+                  {pow :t {+ :x 0.5}}
+                  {exp -:t}
+                  {gamma.rec :x {A.first {gamma.p}} 1}}
+}}}}
+-> gamma
+
+{S.map {lambda {:i}
+               {div} Γ(:i) = {gamma :i}}
+       {S.serie -5.5 5.5 0.5}}
+
+ Γ(-5.5) = 0.010912654781909836
+ Γ(-5) = -42755084646679.17
+ Γ(-4.5) = -0.06001960130050417
+ Γ(-4) = 267219279041745.34
+ Γ(-3.5) = 0.27008820585226917
+ Γ(-3) = -1425169488222640
+ Γ(-2.5) = -0.9453087204829418
+ Γ(-2) = 6413262697001885
+ Γ(-1.5) = 2.363271801207352
+ Γ(-1) = -25653050788007544
+ Γ(-0.5) = -3.5449077018110295
+ Γ(0) = Infinity
+ Γ(0.5) = 1.7724538509055159
+ Γ(1) = 0.9999999999999998
+ Γ(1.5) = 0.8862269254527586
+ Γ(2) = 1.0000000000000002
+ Γ(2.5) = 1.3293403881791384
+ Γ(3) = 2.000000000000001
+ Γ(3.5) = 3.3233509704478426
+ Γ(4) = 6.000000000000007
+ Γ(4.5) = 11.631728396567446
+ Γ(5) = 23.999999999999996
+ Γ(5.5) = 52.34277778455358