jacobiSD

Jacobi SD elliptic function

Description

example

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

Examples

Calculate Jacobi SD Elliptic Function for Numeric Inputs

jacobiSD(2,1)
ans =
    3.6269

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

jacobiSD([2 1 -3],[1 2 3])
ans =
    3.6269    2.1629 -126.3078

Calculate Jacobi SD Elliptic Function for Symbolic Numbers

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

jacobiSD(sym(2),sym(1))
ans =
sinh(2)

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

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

Find Jacobi SD Elliptic Function for Symbolic Variables or Expressions

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

syms x y
f = jacobiSD(x,y)
f =
jacobiSD(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 =
jacobiSD(3, 5)
fVal = double(f)
fVal =
    0.0312

Calculate f to higher precision using vpa.

fVal = vpa(f)
fVal =
0.031220579864538785956650143970485

Plot Jacobi SD Elliptic Function

Plot the Jacobi SD 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) = jacobiSD(u,m);
fcontour(f,'Fill','on')
title('Jacobi SD 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.

More About

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Jacobi SD Elliptic Function

The Jacobi SD elliptic function is

sd(u,m) = sn(u,m)/dn(u,m)

where sn and dn 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.

Introduced in R2017b