wp {jacobi}

Weierstrass elliptic function

Description

Evaluation of the Weierstrass elliptic function and its derivatives.

Usage

wp(z, g = NULL, omega = NULL, tau = NULL, derivative = 0L)

Arguments

z

complex number, vector or matrix

g

the elliptic invariants, a vector of two complex numbers; only one of g, omega and tau must be given

omega

the half-periods, a vector of two complex numbers; only one of g, omega and tau must be given

tau

the half-periods ratio; supplying tau is equivalent to supply omega = c(1/2, tau/2)

derivative

differentiation order, an integer between 0 and 3

Value

A complex number, vector or matrix.

Examples

omega1 <- 1.4 - 1i
omega2 <- 1.6 + 0.5i
omega <- c(omega1, omega2)
e1 <- wp(omega1, omega = omega)
e2 <- wp(omega2, omega = omega)
e3 <- wp(-omega1-omega2, omega = omega)
e1 + e2 + e3 # should be 0