Data update

Task/Gamma-function/DuckDB/gamma-function.duckdb

@@ -0,0 +1,30 @@
+create or replace function gamma_taylor(x) as (
+  select gamma
+  from ( select [
+    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,
+    length(a) as n,
+    (with recursive cte as (
+       select 2 as an, a[n] as acc
+       union all
+       select an+1 as an,
+         (acc * (x-1)) + a[1 + n-an] as acc
+       from cte
+       where an <= n
+     )
+     select 1 / last(acc order by an) from cte) as gamma
+  )
+  limit 1
+);
+
+## Comparison
+select x, gamma, taylor, 2 * @(gamma-taylor)/(gamma+taylor) as "%"
+from (select x, gamma(x) as gamma, gamma_taylor(x) as taylor
+      from (select x/3 as x from range(1,11) t(x))) ;