jacobiCN

Jacobi CN elliptic function

Syntax

jacobiCN(u,m)

Description

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

Examples

Calculate Jacobi CN Elliptic Function for Numeric Inputs

jacobiCN(2,1)

ans =
    0.2658

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

jacobiCN([2 1 -3],[1 2 3])

ans =
    0.2658    0.7405    0.8165

Calculate Jacobi CN Elliptic Function for Symbolic Numbers

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

jacobiCN(sym(2),sym(1))

ans =
1/cosh(2)

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

jacobiCN(sym(2),sym(3))

ans =
jacobiCN(2, 3)

Find Jacobi CN Elliptic Function for Symbolic Variables or Expressions

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

syms x y
f = jacobiCN(x,y)

f =
jacobiCN(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 =
jacobiCN(3, 5)

fVal = double(f)

fVal =
    0.9995

Calculate f to higher precision using vpa.

fVal = vpa(f)

fVal =
0.9995148837279268257000709197021

Plot Jacobi CN Elliptic Function

Plot the Jacobi CN 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) = jacobiCN(u,m);
fcontour(f,'Fill','on')
title('Jacobi CN Elliptic Function')
xlabel('u')
ylabel('m')

Input Arguments

u — Input

number | vector | matrix | multidimensional array | symbolic number | symbolic variable | symbolic vector | symbolic matrix | symbolic multidimensional array | symbolic function | symbolic expression

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

m — Input

number | vector | matrix | multidimensional array | symbolic number | symbolic variable | symbolic vector | symbolic matrix | symbolic multidimensional array | symbolic function | symbolic 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

Jacobi CN Elliptic Function

The Jacobi CN elliptic function is cn(u,m) = cos(am(u,m)) where am is the Jacobi amplitude 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.

Version History

Introduced in R2017b