nag_scaled_log_gamma (s14ahc) (PDF version)
s Chapter Contents
s Chapter Introduction
NAG C Library Manual

NAG Library Function Document

nag_scaled_log_gamma (s14ahc)

+ Contents

    1  Purpose
    7  Accuracy

1  Purpose

nag_scaled_log_gamma (s14ahc) returns the value of lnGx, the scaled logarithm of the gamma function Γx.

2  Specification

#include <nag.h>
#include <nags.h>
double  nag_scaled_log_gamma (double x, NagError *fail)

3  Description

nag_scaled_log_gamma (s14ahc) calculates an approximate value for lnGx, where Gx=Γx+1/xex. This is a variant of the lnΓx function (see also nag_log_gamma (s14abc)), which avoids rounding problems for very large arguments by computing lnΓx with the Stirling approximation factored out.
For 0<x<15, lnGx=lnΓx+1-xlnx+x;
and for 15x, lnGx=12 lnx+ln2π+1xR1/x2, where R is a suitable Remez approximation.
For x0.0, the value lnGx is undefined; nag_scaled_log_gamma (s14ahc) returns zero and exits with fail.code= NE_REAL_ARG_LE.

4  References

Abramowitz M and Stegun I A (1972) Handbook of Mathematical Functions (3rd Edition) Dover Publications

5  Arguments

1:     xdoubleInput
On entry: the argument x of the function.
Constraint: x>0.0.
2:     failNagError *Input/Output
The NAG error argument (see Section 3.6 in the Essential Introduction).

6  Error Indicators and Warnings

NE_INTERNAL_ERROR
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.
NE_REAL_ARG_LE
On entry, x=value.
Constraint: x>0.0.

7  Accuracy

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.

8  Further Comments

None.

9  Example

This example reads values of the argument x from a file, evaluates the function at each value of x and prints the results.

9.1  Program Text

Program Text (s14ahce.c)

9.2  Program Data

Program Data (s14ahce.d)

9.3  Program Results

Program Results (s14ahce.r)


nag_scaled_log_gamma (s14ahc) (PDF version)
s Chapter Contents
s Chapter Introduction
NAG C Library Manual

© The Numerical Algorithms Group Ltd, Oxford, UK. 2012