jacobiCS

Jacobi CS elliptic function

Description

example

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

Examples

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jacobiCS(2,1)
ans =
0.2757

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

jacobiCS([2 1 -3],[1 2 3])
ans =
0.2757    1.1017    1.4142

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

jacobiCS(sym(2),sym(1))
ans =
1/sinh(2)

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

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

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

syms x y
f = jacobiCS(x,y)
f =
jacobiCS(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 =
jacobiCS(3, 5)
fVal = double(f)
fVal =
32.0925

Calculate f to higher precision using vpa.

fVal = vpa(f)
fVal =
32.092535022751828816106562829547

Plot the Jacobi CS 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) = jacobiCS(u,m);
fcontour(f,'Fill','on')
title('Jacobi CS Elliptic Function')
xlabel('u')
ylabel('m') Input Arguments

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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.

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Jacobi CS Elliptic Function

The Jacobi CS elliptic function is

cs(u,m) = cn(u,m)/sn(u,m)

where cn and sn are the respective Jacobi elliptic functions.

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.