jellip {jacobi}

Jacobi elliptic functions

Description

Evaluation of the Jacobi elliptic functions.

Usage

jellip(kind, u, tau = NULL, m = NULL)

Arguments

kind

a string with two characters among "s", "c", "d" and "n"; this string specifies the function: the two letters respectively denote the basic functions sn, cn, dn and 1, and the string specifies the ratio of two such functions, e.g. ns = 1/sn and cd = cn/dn

u

a complex number, vector or matrix

tau

complex number with strictly positive imaginary part; it is related to m and only one of them must be supplied

m

the "parameter", square of the elliptic modulus; it is related to tau and only one of them must be supplied

Value

A complex number, vector or matrix.

Examples

u <- 2 + 2i
tau <- 1i
jellip("cn", u, tau)^2 + jellip("sn", u, tau)^2 # should be 1