NAG CL Interface
s14ahc (gamma_​log_​scaled_​real)

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1 Purpose

s14ahc returns the value of lnG(x), the scaled logarithm of the gamma function Γ(x).

2 Specification

#include <nag.h>
double  s14ahc (double x, NagError *fail)
The function may be called by the names: s14ahc, nag_specfun_gamma_log_scaled_real or nag_scaled_log_gamma.

3 Description

s14ahc calculates an approximate value for lnG(x), where G(x)=Γ(x+1)/(xe)x. This is a variant of the lnΓ(x) function (see also s14abc), which avoids rounding problems for very large arguments by computing lnΓ(x) with the Stirling approximation factored out.
For 0<x<15, lnG(x)=lnΓ(x+1)-xlnx+x;
and for 15x, lnG(x)=12 lnx+ln(2π)+1xR(1/x2), where R is a suitable Remez approximation.
For x0.0, the value lnG(x) is undefined; s14ahc returns zero and exits with fail.code= NE_REAL_ARG_LE.

4 References

NIST Digital Library of Mathematical Functions

5 Arguments

1: x double Input
On entry: the argument x of the function.
Constraint: x>0.0.
2: fail NagError * Input/Output
The NAG error argument (see Section 7 in the Introduction to the NAG Library CL Interface).

6 Error Indicators and Warnings

Dynamic memory allocation failed.
See Section 3.1.2 in the Introduction to the NAG Library CL Interface 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 7.5 in the Introduction to the NAG Library CL Interface for further information.
Your licence key may have expired or may not have been installed correctly.
See Section 8 in the Introduction to the NAG Library CL Interface for further information.
On entry, x=value.
Constraint: x>0.0.

7 Accuracy

s14ahc has been designed to produce full relative accuracy for all input arguments. Empirical results obtained by comparing with multiprecision software confirm this.

8 Parallelism and Performance

Background information to multithreading can be found in the Multithreading documentation.
s14ahc is not threaded in any implementation.

9 Further Comments


10 Example

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

10.1 Program Text

Program Text (s14ahce.c)

10.2 Program Data

Program Data (s14ahce.d)

10.3 Program Results

Program Results (s14ahce.r)
GnuplotProduced by GNUPLOT 5.4 patchlevel 6 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 0 1 2 3 4 5 6 7 8 lnG(x) x "s14ahfe.r" Example Program Returns the Value of lnG(x), the Scaled Logarithm of the Gamma Function Γ(x)