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

Table of contents


NAME

ellref, ellre, ellrel, ellrew, ellreq, ellrell, ellredf, ellred, ellredl, ellredll - incomplete elliptic integral function

SYNOPSIS

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

#include <mathcw.h>

extern float ellref (float x, float y);

extern double ellre (double x, double y);

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

extern __float80 ellrew (__float80 x, __float80 y);

extern __float128 ellreq (__float128 x, __float128 y);

extern long_long_double ellrell (long_long_double x, long_long_double y);

extern decimal_float ellredf (decimal_float x, decimal_float y);

extern decimal_double ellred (decimal_double x, decimal_double y);

extern decimal_long_double ellredl (decimal_long_double x, decimal_long_double y);

extern decimal_long_long_double ellredll (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
ellre(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 = (4 / pi) * ellrg(x, y, 0)
where x >= 0 and y > 0.

The function is symmetric in x and y.

The integral diverges, so the ellrg() form is used.

The normalization condition satisfied is

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