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

Table of contents


NAME

ellrkf, ellrk, ellrkl, ellrkw, ellrkq, ellrkll, ellrkdf, ellrkd, ellrkdl, ellrkdll - incomplete elliptic integral function

SYNOPSIS

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

#include <mathcw.h>

extern float ellrkf (float x, float y);

extern double ellrk (double x, double y);

extern long double ellrkl (long double x, long double y);

extern __float80 ellrkw (__float80 x, __float80 y);

extern __float128 ellrkq (__float128 x, __float128 y);

extern long_long_double ellrkll (long_long_double x, long_long_double y);

extern decimal_float ellrkdf (decimal_float x, decimal_float y);

extern decimal_double ellrkd (decimal_double x, decimal_double y);

extern decimal_long_double ellrkdl (decimal_long_double x, decimal_long_double y);

extern decimal_long_long_double ellrkdll (decimal_long_long_double x, decimal_long_long_double y);

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
ellrk(x, y) = R(1/2; 1/2, 1/2; x, y) = (1/pi) * integral(t=0:Infinity) t**(-1/2) * (t + x)**(-1/2) * (t + y)**(-1/2) dt = (2 / pi) * ellrf(x, y, 0) = (2 / ( pi * sqrt(y))) * ellk(sqrt((y - x) / y))
where x >= 0 and y > 0.

The function is symmetric in x and y.

The normalization condition satisfied is

ellrk(x, x) = x**(-1/2).

RETURN VALUES

Return the value of the incomplete elliptic integral function.

ERRORS

If either 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), ellrl(3CW), ellrm(3CW), elq(3CW), elq1p(3CW), elqc(3CW), elqc1p(3CW).