ELWZ 3CW "01 March 2010" "mathcw-1.00"

Table of contents


NAME

elwzf, elwz, elwzl, elwzw, elwzq, elwzll, elwzdf, elwzd, elwzdl, elwzdll - Weierstrass zeta function

SYNOPSIS

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

#include <mathcw.h>

extern float elwzf (float u, float e1, float e2);

extern double elwz (double u, double e1, double e2);

extern long double elwzl (long double u, long double e1, long double e2);

extern __float80 elwzw (__float80 u, __float80 e1, __float80 e2);

extern __float128 elwzq (__float128 u, __float128 e1, __float128 e2);

extern long_long_double elwzll (long_long_double u,
                    long_long_double e1, long_long_double e2);

extern decimal_float elwzdf (decimal_float u,
                    decimal_float e1, decimal_float e2);

extern decimal_double elwzd (decimal_double u,
                   decimal_double e1, decimal_double e2);

extern decimal_long_double elwzdl (decimal_long_double u,
                    decimal_long_double e1, decimal_long_double e2);

extern decimal_long_long_double elwzdll (decimal_long_long_double u,
                    decimal_long_long_double e1, decimal_long_long_double e2);

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


DESCRIPTION

Given e1 and e2, which are any two of the three roots of the Weierstrass cubic polynomial, where the sum of the roots is zero, compute the Weierstrass zeta function, zeta(u,e1,e2).

The argument u is unrestricted, but function accuracy deteriorates severely for u values outside the periods of the Weierstrass elliptic function. The periods can be found with elwo(3CW).

Mathematical texts commonly parameterize the Weierstrass functions with the cubic polynomial coefficents g2 and g3, instead of the roots e1 and e2. Convert between the two argument conventions with elwe(3CW) and elwg(3CW).

See M. Abramowitz & I. A. Stegun, Handbook of Mathematical Functions, Chapter 18, for definitions of the Weierstrass elliptic, sigma, and zeta functions.


RETURN VALUES

Return the value of the Weierstrass elliptic function.

ERRORS

If any argument is a NaN, set the result to that argument.

SEE ALSO

elk(3CW), elkm1(3CW), elq(3CW), elq1p(3CW), elqc(3CW), elqc1p(3CW), elwdp(3CW), elwe(3CW), elwg(3CW), elwip(3CW), elwk(3CW), elwo(3CW), elwp(3CW), elws(3CW),