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

Table of contents


NAME

ellrdf, ellrd, ellrdl, ellrdw, ellrdq, ellrdll, ellrddf, ellrdd, ellrddl, ellrddll - incomplete elliptic integral function

SYNOPSIS

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

#include <mathcw.h>

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

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

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

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

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

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

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

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

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

extern decimal_long_long_double ellrddll (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
ellrd(x, y, z) = R(3/2; 1/2, 1/2, 3/2; x, y, z) = (3/2) * integral(t=0:Infinity) (t + x)**(-1/2) * (t + y)**(-1/2) * (t + z)**(-3/2) dt = ellrf(x, y, z, z)
where x >= 0, y > 0, and z > 0.

The normalization condition satisfied is

ellrd(x, x, x) = x**(-3/2).

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), ellre(3CW), ellrf(3CW), ellrg(3CW), ellrh(3CW), ellrj(3CW), ellrk(3CW), ellrl(3CW), ellrm(3CW), elq(3CW), elq1p(3CW), elqc(3CW), elqc1p(3CW).