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

Table of contents


NAME

ellrlf, ellrl, ellrll, ellrlw, ellrlq, ellrlll, ellrldf, ellrld, ellrldl, ellrldll - incomplete elliptic integral function

SYNOPSIS

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

#include <mathcw.h>

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

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

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

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

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

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

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

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

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

extern decimal_long_long_double ellrldll (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
ellrl(x, y, rho) = R(1/2; 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 = (8 / (3 * pi)) * ellrh(x, y, 0, rho)
where x >= 0, y > 0, and rho > 0.

The function is symmetric in x and y.

The normalization condition satisfied is

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