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

Table of contents


NAME

ellrhf, ellrh, ellrhl, ellrhw, ellrhq, ellrhll, ellrhdf, ellrhd, ellrhdl, ellrhdll - incomplete elliptic integral function

SYNOPSIS

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

#include <mathcw.h>

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

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

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

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

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

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

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

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

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

extern decimal_long_long_double ellrhdll (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
ellrh(x, y, z, rho) = R(1/2; 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) * t * dt = (3/2) * ellrf(x, y, z) - (1/2) * rho * ellrj(x, y, z, rho)
where x >= 0, y > 0, z > 0, and rho > 0.

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

The normalization condition satisfied is

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