nag_scaled_log_gamma (s14ahc) calculates an approximate value for , where . This is a variant of the function (see also nag_log_gamma (s14abc)), which avoids rounding problems for very large arguments by computing with the Stirling approximation factored out.
For , ;
and for , , where is a suitable Remez approximation.
For , the value is undefined; nag_scaled_log_gamma (s14ahc) returns zero and exits with NE_REAL_ARG_LE.
Abramowitz M and Stegun I A (1972) Handbook of Mathematical Functions (3rd Edition) Dover Publications
On entry: the argument of the function.
– NagError *Input/Output
The NAG error argument (see Section 3.7 in How to Use the NAG Library and its Documentation).
Error Indicators and Warnings
Dynamic memory allocation failed.
See Section 220.127.116.11 in How to Use the NAG Library and its Documentation for further information.
An internal error has occurred in this function. Check the function call and any array sizes. If the call is correct then please contact NAG for assistance.
See Section 2.7.6 in How to Use the NAG Library and its Documentation for further information.
Your licence key may have expired or may not have been installed correctly.
See Section 2.7.5 in How to Use the NAG Library and its Documentation for further information.
On entry, .
nag_scaled_log_gamma (s14ahc) has been designed to produce full relative accuracy for all input arguments. Empirical results obtained by comparing with multiprecision software confirm this.
Parallelism and Performance
nag_scaled_log_gamma (s14ahc) is not threaded in any implementation.
This example reads values of the argument from a file, evaluates the function at each value of and prints the results.