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.
ellfi(phi,k) = integral(t=0:phi) (1 - (k * sin(t))**2)**(-1/2) dtwhere 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]