BETAM1 3CW "28 December 2009" "mathcw-1.00"

Table of contents


NAME

betam1 - Catalan/Dirichlet beta function, less 1

SYNOPSIS

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

#include <mathcw.h>

extern float betam1f (float);

extern double betam1 (double);

extern long double betam1l (long double);

extern __float80 betam1w (__float80);

extern __float128 betam1q (__float128);

extern long_long_double betam1ll (long_long_double);

extern decimal_float betam1df (decimal_float);

extern decimal_double betam1d (decimal_double);

extern decimal_long_double betam1dl (decimal_long_double);

extern decimal_long_long_double betam1dll (decimal_long_long_double);

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


DESCRIPTION

Determine the value of the Catalan/Dirichlet beta function, less 1, betam1(x).

These values are defined by the relations

beta(x)   = sum(k = 1:Infinity) (-1)**k (2k - 1)**(-x),
betam1(x) = beta(x) - 1,
betam1(x) = sum(k = 2:Infinity) (-1)**k (2k - 1)**(-x).

Whole-number arguments are special cases that are computed internally, and quickly, by a call to betnm1(3CW).

For large positive x, the value of beta(x) approaches 1 from below, so this function, betam1(x) should then be used to compute the difference beta(x) - 1 accurately.


RETURN VALUES

Return the Catalan/Dirichlet beta function value.

ERRORS

If the argument is a NaN, set errno to EDOM and return that argument.

If the argument is -Infinity, set errno to ERANGE and return +Infinity.


SEE ALSO

bernum(3CW), beta(3CW), betnm1(3CW), betnum(3CW), eulnum(3CW), fibnum(3CW), zeta(3CW), zetam1(3CW), zetnm1(3CW), zetnum(3CW).