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))) ;