H. T. Davis Gamma(x)

a2913395-2361-484e-85e8-87a6261eb351 2 15 12 decimal

&[DATE] &[TIME] - &[FILENAME]

Abramowitz & Stegun, p. 256 c 1 0.5772156649015329 0.6558780715202538 - 0.0420026350340952 - 0.1665386113822915 0.0421977345555443 - 0.0096219715278770 - 0.0072189432466630 0.0011651675918591 - 0.0002152416741149 - 0.0001280502823882 0.0000201348547807 - 0.0000012504934821 - 0.0000011330272320 0.0000002056338417 - 0.0000000061160950 0.0000000050020075 0.0000000011812746 - 0.0000000001043427 0.0000000000077823 0.0000000000036968 - 0.0000000000005100 0.0000000000000206 - 0.0000000000000054 - 0.0000000000000014 0.0000000000000001 261 mat :

1 z Γ / c k el z k^* k 1 ∞ sum ≡

z Γpoly c k el z k^* k 126 sum :

z Γa 1 z Γpoly / :

x c 10 x ≤ (x 1 ≤ (& cases :

x Γa x c * 1 1 + 15 red 1 5 mat 2 1 sys if/otherwise NOT used ... for reference

Gamma(x)

constant 15 D accuracy @ integers x Γ x Γa 0 x ≤ (x 1 ≤ (& x 1 - (x 1 - Γa * 1 x ≤ (x 2 ≤ (& x 2 - (x 1 - (* x 2 - Γa * 2 x ≤ (x 3 ≤ (& x 3 - (x 2 - (* x 1 - (* x 3 - Γa * 3 x ≤ (x 4 ≤ (& x 4 - (x 3 - (* x 2 - (* x 1 - (* x 4 - Γa * 4 x ≤ (x 5 ≤ (& x 5 - (x 4 - (* x 3 - (* x 2 - (* x 1 - (* x 5 - Γa * 5 x ≤ (x 6 ≤ (& x 6 - (x 5 - (* x 4 - (* x 3 - (* x 2 - (* x 1 - (* x 6 - Γa * 6 x ≤ (x 7 ≤ (& x 7 - (x 6 - (* x 5 - (* x 4 - (* x 3 - (* x 2 - (* x 1 - (* x 7 - Γa * 7 x ≤ (x 8 ≤ (& x 8 - (x 7 - (* x 6 - (* x 5 - (* x 4 - (* x 3 - (* x 2 - (* x 1 - (* x 8 - Γa * 8 x ≤ (x 9 ≤ (& x 9 - (x 8 - (* x 7 - (* x 6 - (* x 5 - (* x 4 - (* x 3 - (* x 2 - (* x 1 - (* x 9 - Γa * 9 x ≤ (x 10 ≤ (& undefined cases :

e Γ 1.56746825577405

5 Γ 24

9.5 Γ 119292.461994609

x Γ