Data commit

Task/Gamma-function/Jq/gamma-function-1.jq

@@ -0,0 +1,16 @@
+def gamma:
+  [
+    1.00000000000000000000,  0.57721566490153286061,  -0.65587807152025388108, -0.04200263503409523553,
+    0.16653861138229148950, -0.04219773455554433675,  -0.00962197152787697356,  0.00721894324666309954,
+   -0.00116516759185906511, -0.00021524167411495097,   0.00012805028238811619, -0.00002013485478078824,
+   -0.00000125049348214267,  0.00000113302723198170,  -0.00000020563384169776,  0.00000000611609510448,
+    0.00000000500200764447, -0.00000000118127457049,   0.00000000010434267117,  0.00000000000778226344,
+   -0.00000000000369680562,  0.00000000000051003703,  -0.00000000000002058326, -0.00000000000000534812,
+    0.00000000000000122678, -0.00000000000000011813,   0.00000000000000000119,  0.00000000000000000141,
+   -0.00000000000000000023,  0.00000000000000000002
+  ] as $a
+  | (. - 1) as $y
+  | ($a|length) as $n
+  | reduce range(2; 1+$n) as $an
+      ($a[$n-1]; (. * $y) + $a[$n - $an])
+  | 1 / . ;

Task/Gamma-function/Jq/gamma-function-2.jq

@@ -0,0 +1,16 @@
+# for reals, but easily extended to complex values
+def gamma_by_lanczos:
+  def pow(x): if x == 0 then 1 elif x == 1 then . else x * log | exp end;
+  . as $x
+  | ((1|atan) * 4) as $pi
+  | if $x < 0.5 then $pi / ((($pi * $x) | sin) * ((1-$x)|gamma_by_lanczos ))
+    else
+      [   0.99999999999980993, 676.5203681218851,     -1259.1392167224028,
+        771.32342877765313,   -176.61502916214059,       12.507343278686905,
+         -0.13857109526572012,   9.9843695780195716e-6,   1.5056327351493116e-7] as $p
+    | ($x - 1) as $x
+    | ($x + 7.5) as $t
+    |  reduce range(1; $p|length) as $i
+          ($p[0]; . + ($p[$i]/($x + $i) ))
+       * ((2*$pi) | sqrt) * ($t | pow($x+0.5)) * ((-$t)|exp)
+    end;

Task/Gamma-function/Jq/gamma-function-3.jq

@@ -0,0 +1,5 @@
+def gamma_by_stirling:
+  def pow(x): if x == 0 then 1 elif x == 1 then . else x * log | exp end;
+  ((1|atan) * 8) as $twopi
+  | . as $x
+  | (($twopi/$x) | sqrt) * ( ($x / (1|exp)) | pow($x));

Task/Gamma-function/Jq/gamma-function-4.jq

@@ -0,0 +1,6 @@
+def pad(n): tostring | . + (n - length) * " ";
+
+"                 i:      gamma                lanczos              tgamma",
+(range(1;11)
+ | . / 3.0
+ | "\(pad(18)): \(gamma|pad(18)) : \(gamma_by_lanczos|pad(18)) : \(tgamma)")

Task/Gamma-function/Jq/gamma-function-5.jq

@@ -0,0 +1,12 @@
+$ jq -M -r -n -f Gamma_function_Stirling.jq
+                 i:      gamma                lanczos              tgamma
+0.3333333333333333: 2.6789385347077483 : 2.6789385347077483 : 2.678938534707748
+0.6666666666666666: 1.3541179394264005 : 1.3541179394263998 : 1.3541179394264005
+1                 : 1                  : 0.9999999999999998 : 1
+1.3333333333333333: 0.8929795115692493 : 0.8929795115692494 : 0.8929795115692493
+1.6666666666666667: 0.9027452929509336 : 0.9027452929509342 : 0.9027452929509336
+2                 : 1                  : 1.0000000000000002 : 1
+2.3333333333333335: 1.190639348758999  : 1.1906393487589995 : 1.190639348758999
+2.6666666666666665: 1.5045754882515399 : 1.5045754882515576 : 1.5045754882515558
+3                 : 1.9999999999939684 : 2.0000000000000013 : 2
+3.3333333333333335: 2.778158479338573  : 2.778158480437665  : 2.7781584804376647