ELLE 3CW "11 October 2007" "mathcw-1.00"

Table of contents


NAME

ellef, elle, ellel, ellew, elleq, ellell, elledf, elled, elledl, elledll - complete elliptic integral function of the second kind

SYNOPSIS

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

#include <mathcw.h>

extern float ellef (float x);

extern double elle (double x);

extern long double ellel (long double x);

extern __float80 ellew (__float80 x);

extern __float128 elleq (__float128 x);

extern long_long_double ellell (long_long_double x);

extern decimal_float elledf (decimal_float x);

extern decimal_double elled (decimal_double x);

extern decimal_long_double elledl (decimal_long_double x);

extern decimal_long_long_double elledll (decimal_long_long_double x);

NB: Functions with prototypes containing underscores in type names may be available only with certain extended compilers.


DESCRIPTION

Compute the complete elliptic integral function of the second kind, defined by
elle(x) = integral(t=0:pi/2) sqrt(1 - x**2 * sin(t)**2) dt
where x is in [-1,+1].

Equivalents in other systems are:

Abramowitz & Stegun NBS Handbook #55: E(m) = elle(sqrt(m)) Mathematica: EllipticE[x] = elle(sqrt(x)) Maple: EllipticE(x) = elle(x)

RETURN VALUES

Return the complete elliptic integral function of the second kind.

ERRORS

If the argument is a NaN, return that argument and set errno to EDOM. If the argument is out of the range [-1,+1], return a NaN and set errno to EDOM.

SEE ALSO

agm(3CW), elk(3CW), elkm1(3CW), ellec(3CW), ellk(3CW), ellkc(3CW), elq(3CW), elq1p(3CW), elqc(3CW), elqc1p(3CW).