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

Table of contents


NAME

ellkcf, ellkc, ellkcl, ellkcw, ellkcq, ellkcll, ellkcdf, ellkcd, ellkcdl, ellkcdll - complementary complete elliptic integral function of the first kind

SYNOPSIS

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

#include <mathcw.h>

extern float ellkcf (float x);

extern double ellkc (double x);

extern long double ellkcl (long double x);

extern __float80 ellkcw (__float80 x);

extern __float128 ellkcq (__float128 x);

extern long_long_double ellkcll (long_long_double x);

extern decimal_float ellkcdf (decimal_float x);

extern decimal_double ellkcd (decimal_double x);

extern decimal_long_double ellkcdl (decimal_long_double x);

extern decimal_long_long_double ellkcdll (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 complementary complete elliptic integral function of the first kind, defined by
ellkc(x) = integral(t=0:pi/2) (1 / sqrt(1 - (1 - x**2) * sin(t)**2)) dt
where x is in [-1,+1].

Equivalents in other systems are:

Abramowitz & Stegun NBS Handbook #55: K'(m) = ellkc(sqrt(m)) Mathematica: EllipticK[x] = ellkc(sqrt(1 - x)) Maple: EllipticCK(x) = ellkc(x)

RETURN VALUES

Return the complementary complete elliptic integral function of the first kind.

ERRORS

If the argument is a NaN, set errno to EDOM and return that argument. If the argument is out of the range [-1,+1], set errno to EDOM and return a NaN. If the argument is 0, return Infinity and set errno to ERANGE.

SEE ALSO

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