BETNM1 3CW "26 December 2009" "mathcw-1.00"

Table of contents


NAME

betnm1 - n-th Catalan/Dirichlet beta number, less 1

SYNOPSIS

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

#include <mathcw.h>

extern float betnm1f (int n);

extern double betnm1 (int n);

extern long double betnm1l (int n);

extern __float80 betnm1w (int n);

extern __float128 betnm1q (int n);

extern long_long_double betnm1ll (int n);

extern decimal_float betnm1df (int n);

extern decimal_double betnm1d (int n);

extern decimal_long_double betnm1dl (int n);

extern decimal_long_long_double betnm1dll (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, less 1, by fast table lookup.

The Catalan/Dirichlet beta function is defined by

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

For positive arguments, its values rapidly approach 1. Consequently, this function returns an accurate value of the difference beta(n) - 1. That relation is equivalent to

betam1(n) = sum(k = 2:Infinity) (-1)**(k - 1) * (2*k - 1)**(-n).

RETURN VALUES

Return the n-th Catalan/Dirichlet beta number, less 1.

ERRORS

None.

SEE ALSO

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