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

Table of contents


NAME

elwdpf, elwdp, elwdpl, elwdpw, elwdpq, elwdpll, elwdpdf, elwdpd, elwdpdl, elwdpdll - first derivative of Weierstrass elliptic function

SYNOPSIS

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

#include <mathcw.h>

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

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

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

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

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

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

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

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

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

extern decimal_long_long_double elwdpdll (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 first derivative with respect to u of the Weierstrass elliptic function, p'(u,e1,e2) = dp(u,e1,e2)/du.

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).

The letter p in the Weierstrass elliptic function name is conventionally represented by a stylized script letter, although typographical limitations sometimes force it to be a calligraphic or fraktur letter.

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 first derivative 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), elwe(3CW), elwg(3CW), elwip(3CW), elwk(3CW), elwo(3CW), elwp(3CW), elws(3CW), elwz(3CW),