Comments from Z. Yang: Returns ln(gamma(alpha)) for alpha>0, accurate to 10 decimal places. Stirling's formula is used for the central polynomial part of the procedure. Pike MC & Hill ID (1966) Algorithm 291: Logarithm of the gamma function. Communications of the Association for Computing Machinery, 9:684

_incomplete_gamma(x, alpha)

source code

Compute an incomplete gamma ratio.

Comments from Z. Yang:
Returns the incomplete gamma ratio I(x,alpha) where x is the upper 
       limit of the integration and alpha is the shape parameter.
returns (-1) if in error
ln_gamma_alpha = ln(Gamma(alpha)), is almost redundant.
(1) series expansion     if alpha>x or x<=1
(2) continued fraction   otherwise
RATNEST FORTRAN by
Bhattacharjee GP (1970) The incomplete gamma integral.  Applied Statistics,
19: 285-287 (AS32)