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

Table of contents


NAME

ellkf, ellk, ellkl, ellkw, ellkq, ellkll, ellkdf, ellkd, ellkdl, ellkdll - complete elliptic integral function of the first kind from modulus

SYNOPSIS

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

#include <mathcw.h>

extern float ellkf (float x);

extern double ellk (double x);

extern long double ellkl (long double x);

extern __float80 ellkw (__float80 x);

extern __float128 ellkq (__float128 x);

extern long_long_double ellkll (long_long_double x);

extern decimal_float ellkdf (decimal_float x);

extern decimal_double ellkd (decimal_double x);

extern decimal_long_double ellkdl (decimal_long_double x);

extern decimal_long_long_double ellkdll (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 first kind, defined by
ellk(x) = integral(t=0:pi/2) (1 / sqrt(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) = ellk(sqrt(m)) Mathematica: EllipticK[x] = ellk(sqrt(x)) Maple: EllipticK(x) = ellk(x)

RETURN VALUES

Return the complete elliptic integral function of the first 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. If the argument is +1 or -1, return Infinity and set errno to ERANGE.

SEE ALSO

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