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

Table of contents


NAME

eljamf, eljam, eljaml, eljamw, eljamq, eljamll, eljamdf, eljamd, eljamdl, eljamdll - Jacobian elliptic function

SYNOPSIS

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

#include <mathcw.h>

extern float eljamf (float u, float k);

extern double eljam (double u, double k);

extern long double eljaml (long double u, long double k);

extern __float80 eljamw (__float80 u, __float80 k);

extern __float128 eljamq (__float128 u, __float128 k);

extern long_long_double eljamll (long_long_double u, long_long_double k);

extern decimal_float eljamdf (decimal_float u, decimal_float k);

extern decimal_double eljamd (decimal_double u, decimal_double k);

extern decimal_long_double eljamdl (decimal_long_double u, decimal_long_double k);

extern decimal_long_long_double eljamdll (decimal_long_long_double u, 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 Jacobian elliptic function amplitude, an angle in [-pi, +pi] such that the Legendre elliptic integral function of the first kind satisfies the relations
k = sin(alpha) u = F(phi \ alpha) = ellfi(phi, k) eljam(u, k) = phi
Thus, the amplitude returned by eljam(u, k) is an inverse of F(phi \ alpha), recovering the angle phi that produces the argument u, where phi also depends on k.

The argument u is unrestricted. The argument k (the modulus) is normally in [-1,+1]. If it is not, then a standard reciprocal modulus transformation is used to convert the function to another with second argument 1/k.

See M. Abramowitz & I. A. Stegun, Handbook of Mathematical Functions, Chapter 16, for definitions of the Jacobian elliptic, theta, and zeta functions.


RETURN VALUES

Return the Jacobian elliptic function amplitude, an angle in [-pi, +pi].

ERRORS

If either argument is a NaN, return that argument. If k is out of range, set errno to EDOM and return a quiet NaN.

SEE ALSO

agm(3CW), eljacd(3CW), eljacn(3CW), eljacs(3CW), eljadc(3CW), eljadn(3CW), eljads(3CW), eljag(3CW), eljanc(3CW), eljand(3CW), eljans(3CW), eljasc(3CW), eljasd(3CW), eljasn(3CW), eljcd(3CW), eljcn(3CW), eljcs(3CW), eljdc(3CW), eljdn(3CW), eljds(3CW), eljh(3CW), eljh4(3CW), eljnc(3CW), eljnd(3CW), eljns(3CW), eljsc(3CW), eljsd(3CW), eljsn(3CW), eljt(3CW), eljt1(3CW), eljt2(3CW), eljt3(3CW), eljt4(3CW), eljta(3CW), eljtd1(3CW), eljtd2(3CW), eljtd3(3CW), eljtd4(3CW), eljtda(3CW), eljz(3CW), elk(3CW), elkm1(3CW), elq(3CW), elq1p(3CW), elqc(3CW), elqc1p(3CW).