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

Table of contents


NAME

ellrmf, ellrm, ellrml, ellrmw, ellrmq, ellrmll, ellrmdf, ellrmd, ellrmdl, ellrmdll - incomplete elliptic integral function

SYNOPSIS

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

#include <mathcw.h>

extern float ellrmf (float x, float y, float rho);

extern double ellrm (double x, double y, double rho);

extern long double ellrml (long double x, long double y, long double rho);

extern __float80 ellrmw (__float80 x, __float80 y, __float80 rho);

extern __float128 ellrmq (__float128 x, __float128 y, __float128 rho);

extern long_long_double ellrmll (long_long_double x, long_long_double y, long_long_double rho);

extern decimal_float ellrmdf (decimal_float x, decimal_float y, decimal_float rho);

extern decimal_double ellrmd (decimal_double x, decimal_double y, decimal_double rho);

extern decimal_long_double ellrmdl (decimal_long_double x, decimal_long_double y, decimal_long_double rho);

extern decimal_long_long_double ellrmdll (decimal_long_long_double x, decimal_long_long_double y, 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
ellrm(x, y, rho) = R(3/2; 1/2, 1/2, 1; x, y, rho) = (2 / pi) * integral(t=0:Infinity) t**(-1/2) * (t + x)**(-1/2) * (t + y)**(-1/2) * (t + rho)**(-1) dt = ellrl(x, y, x * y / rho) / rho
where x >= 0, y > 0, and rho > 0.

The function is symmetric in x and y.

The normalization condition satisfied is

ellrm(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), ellrj(3CW), ellrk(3CW), ellrl(3CW), elq(3CW), elq1p(3CW), elqc(3CW), elqc1p(3CW).