BETNUM 3CW "26 December 2009" "mathcw-1.00"

Table of contents


NAME

betnum - n-th Catalan/Dirichlet beta number

SYNOPSIS

cc [ flags ] -I/usr/local/include file(s) -L/usr/local/lib -lmcw [ ... ]

#include <mathcw.h>

extern float betnumf (int n);

extern double betnum (int n);

extern long double betnuml (int n);

extern __float80 betnumw (int n);

extern __float128 betnumq (int n);

extern long_long_double betnumll (int n);

extern decimal_float betnumdf (int n);

extern decimal_double betnumd (int n);

extern decimal_long_double betnumdl (int n);

extern decimal_long_long_double betnumdll (int n);

NB: Functions with prototypes containing underscores in type names may be available only with certain extended compilers.


DESCRIPTION

Determine the n-th beta number by fast table lookup.

The Catalan/Dirichlet beta function is defined by

beta(n) = sum(k = 1:Infinity) (-1)**(k - 1) * (2k - 1)**(-n).

For positive arguments, its values rapidly approach 1. See betnm1(3CW) for retrieving an accurate value of the difference, beta(n) - 1.


RETURN VALUES

Return the n-th Catalan/Dirichlet beta number.

ERRORS

None.

SEE ALSO

bernum(3CW), beta(3CW), betam1(3CW), betnm1(3CW), eulnum(3CW), fibnum(3CW), zetnm1(3CW), zetnum(3CW).