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

Table of contents


NAME

elleif, ellei, elleil, elleiw, elleiq, elleill, elleidf, elleid, elleidl, elleidll - incomplete 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 elleif (float phi, float k);

extern double ellei (double phi, double k);

extern long double elleil (long double phi, long double k);

extern __float80 elleiw (__float80 phi, __float80 k);

extern __float128 elleiq (__float128 phi, __float128 k);

extern long_long_double elleill (long_long_double phi, long_long_double k);

extern decimal_float elleidf (decimal_float phi, decimal_float k);

extern decimal_double elleid (decimal_double phi, decimal_double k);

extern decimal_long_double elleidl (decimal_long_double phi, decimal_long_double k);

extern decimal_long_long_double elleidll (decimal_long_long_double phi, decimal_long_long_double k);

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


DESCRIPTION

Compute the incomplete elliptic integral function of the second kind defined by
ellei(phi,k) = integral(t=0:phi) (1 - (k * sin(t))**2)**(1/2) dt
where phi is an angle in radians in [0, 2*pi] and k is in [-1,+1].

The Legendre incomplete elliptic function of the second kind in Abramowitz and Stegun's Handbook of Mathematical Functions (Chapter 17 and Table 17.6) can be computed like this:

E(phi \ alpha) = ellei(phi, sin(alpha)).

Equivalents in other systems are:

Maple: E(phi \ alpha) = EllipticE(sin(phi), sin(alpha)) Mathematica: E(phi \ alpha) = EllipticE[phi, (Sin[alpha])^2]

RETURN VALUES

Return the value of the incomplete elliptic integral function of the second kind.

ERRORS

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

SEE ALSO

agm(3CW), elk(3CW), elkm1(3CW), elldi(3CW), elle(3CW), ellec(3CW), ellfi(3CW), ellk(3CW), ellkc(3CW), ellpi(3CW), ellrc(3CW), ellrd(3CW), ellre(3CW), ellrf(3CW), ellrg(3CW), ellrh(3CW), ellrj(3CW), ellrk(3CW), ellrl(3CW), ellrm(3CW), elq(3CW), elq1p(3CW), elqc(3CW), elqc1p(3CW).