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

Table of contents


NAME

ellfif, ellfi, ellfil, ellfiw, ellfiq, ellfill, ellfidf, ellfid, ellfidl, ellfidll - incomplete 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 ellfif (float phi, float k);

extern double ellfi (double phi, double k);

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

extern __float80 ellfiw (__float80 phi, __float80 k);

extern __float128 ellfiq (__float128 phi, __float128 k);

extern long_long_double ellfill (long_long_double phi, long_long_double k);

extern decimal_float ellfidf (decimal_float phi, decimal_float k);

extern decimal_double ellfid (decimal_double phi, decimal_double k);

extern decimal_long_double ellfidl (decimal_long_double phi, decimal_long_double k);

extern decimal_long_long_double ellfidll (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 first kind defined by
ellfi(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 first kind in Abramowitz and Stegun's Handbook of Mathematical Functions (Chapter 17 and Table 17.5) can be computed like this:

F(phi \ alpha) = ellfi(phi, sin(alpha)).

Equivalents in other systems are:

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

RETURN VALUES

Return the value of the incomplete elliptic integral function of the first 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), ellei(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).