ELLRF 3CW "07 February 2010" "mathcw-1.00"

Table of contents


NAME

ellrff, ellrf, ellrfl, ellrfw, ellrfq, ellrfll, ellrfdf, ellrfd, ellrfdl, ellrfdll - incomplete elliptic integral function

SYNOPSIS

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

#include <mathcw.h>

extern float ellrff (float x, float y, float z);

extern double ellrf (double x, double y, double z);

extern long double ellrfl (long double x, long double y, long double z);

extern __float80 ellrfw (__float80 x, __float80 y, __float80 z);

extern __float128 ellrfq (__float128 x, __float128 y, __float128 z);

extern long_long_double ellrfll (long_long_double x, long_long_double y, long_long_double z);

extern decimal_float ellrfdf (decimal_float x, decimal_float y, decimal_float z);

extern decimal_double ellrfd (decimal_double x, decimal_double y, decimal_double z);

extern decimal_long_double ellrfdl (decimal_long_double x, decimal_long_double y, decimal_long_double z);

extern decimal_long_long_double ellrfdll (decimal_long_long_double x, decimal_long_long_double y,
                                          decimal_long_long_double z);

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


DESCRIPTION

Compute the incomplete elliptic integral function defined by
ellrf(x, y, z) = R(1/2; 1/2, 1/2, 1/2; x, y, z) = (1/2) * integral(t=0:Infinity) (t + x)**(-1/2) * (t + y)**(-1/2) * (t + z)**(-1/2) dt
where x >= 0, y > 0, and z > 0.

The normalization condition satisfied is

ellrf(x, x, x) = x**(-1/2).

RETURN VALUES

Return the value of the incomplete elliptic integral function.

ERRORS

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

SEE ALSO

agm(3CW), elk(3CW), elkm1(3CW), elldi(3CW), elle(3CW), ellec(3CW), ellei(3CW), ellfi(3CW), ellk(3CW), ellkc(3CW), ellpi(3CW), ellrc(3CW), ellrd(3CW), ellre(3CW), ellrg(3CW), ellrh(3CW), ellrj(3CW), ellrk(3CW), ellrl(3CW), ellrm(3CW), elq(3CW), elq1p(3CW), elqc(3CW), elqc1p(3CW).