Main Content

jacobiND

Jacobi ND elliptic function

Description

example

jacobiND(u,m) returns the Jacobi ND Elliptic Function of u and m. If u or m is an array, then jacobiND acts element-wise.

Examples

collapse all

jacobiND(2,1)
ans =
    3.7622

Call jacobiND on array inputs. jacobiND acts element-wise when u or m is an array.

jacobiND([2 1 -3],[1 2 3])
ans =
    3.7622    3.2181 -218.7739

Convert numeric input to symbolic form using sym, and find the Jacobi ND elliptic function. For symbolic input where u = 0 or m = 0 or 1, jacobiND returns exact symbolic output.

jacobiND(sym(2),sym(1))
ans =
cosh(2)

Show that for other values of u or m, jacobiND returns an unevaluated function call.

jacobiND(sym(2),sym(3))
ans =
jacobiND(2, 3)

For symbolic variables or expressions, jacobiND returns the unevaluated function call.

syms x y
f = jacobiND(x,y)
f =
jacobiND(x, y)

Substitute values for the variables by using subs, and convert values to double by using double.

f = subs(f, [x y], [3 5])
f =
jacobiND(3, 5)
fVal = double(f)
fVal =
    1.0024

Calculate f to higher precision using vpa.

fVal = vpa(f)
fVal =
1.0024338497055006289470589737758

Plot the Jacobi ND elliptic function using fcontour. Set u on the x-axis and m on the y-axis by using the symbolic function f with the variable order (u,m). Fill plot contours by setting Fill to on.

syms f(u,m)
f(u,m) = jacobiND(u,m);
fcontour(f,'Fill','on')
title('Jacobi ND Elliptic Function')
xlabel('u')
ylabel('m')

Figure contains an axes. The axes with title Jacobi ND Elliptic Function contains an object of type functioncontour.

Input Arguments

collapse all

Input, specified as a number, vector, matrix, or multidimensional array, or a symbolic number, variable, vector, matrix, multidimensional array, function, or expression.

Input, specified as a number, vector, matrix, or multidimensional array, or a symbolic number, variable, vector, matrix, multidimensional array, function, or expression.

More About

collapse all

Jacobi ND Elliptic Function

The Jacobi ND elliptic function is

nd(u,m) = 1/dn(u,m)

where dn is the respective Jacobi elliptic function.

The Jacobi elliptic functions are meromorphic and doubly periodic in their first argument with periods 4K(m) and 4iK'(m), where K is the complete elliptic integral of the first kind, implemented as ellipticK.

Introduced in R2017b