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

Table of contents


NAME

ellrjf, ellrj, ellrjl, ellrjw, ellrjq, ellrjll, ellrjdf, ellrjd, ellrjdl, ellrjdll - incomplete elliptic integral function

SYNOPSIS

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

#include <mathcw.h>

extern float ellrjf (float x, float y, float z, float rho);

extern double ellrj (double x, double y, double z, double rho);

extern long double ellrjl (long double x, long double y, long double z, long double rho);

extern __float80 ellrjw (__float80 x, __float80 y, __float80 z, __float80 rho);

extern __float128 ellrjq (__float128 x, __float128 y, __float128 z, __float128 rho);

extern long_long_double ellrjll (long_long_double x, long_long_double y,
                                 long_long_double z, long_long_double rho);

extern decimal_float ellrjdf (decimal_float x, decimal_float y, decimal_float z, decimal_float rho);

extern decimal_double ellrjd (decimal_double x, decimal_double y, decimal_double z, decimal_double rho);

extern decimal_long_double ellrjdl (decimal_long_double x, decimal_long_double y,
                                    decimal_long_double z, decimal_long_double rho);

extern decimal_long_long_double ellrjdll (decimal_long_long_double x, decimal_long_long_double y,
                                          decimal_long_long_double z, decimal_long_long_double rho);

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
ellrj(x, y, z, rho) = R(3/2; 1/2, 1/2, 1/2, 1; x, y, z, rho) = (3/2) * integral(t=0:Infinity) (t + x)**(-1/2) * (t + y)**(-1/2) * (t + z)**(-1/2) * (t + rho)**(-1) dt
where x >= 0, y > 0, z > 0, and rho > 0.

The function is symmetric in x, y, and z.

The normalization condition satisfied is

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