jacobiNC

Jacobi NC elliptic function

Syntax

``jacobiNC(u,m)``

Description

example

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

Examples

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`jacobiNC(2,1)`
```ans = 3.7622```

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

`jacobiNC([2 1 -3],[1 2 3])`
```ans = 3.7622 1.3505 1.2247```

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

`jacobiNC(sym(2),sym(1))`
```ans = cosh(2)```

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

`jacobiNC(sym(2),sym(3))`
```ans = jacobiNC(2, 3)```

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

```syms x y f = jacobiNC(x,y)```
```f = jacobiNC(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 = jacobiNC(3, 5)```
`fVal = double(f)`
```fVal = 1.0005```

Calculate `f` to higher precision using `vpa`.

`fVal = vpa(f)`
```fVal = 1.0004853517240922102007985618873```

Plot the Jacobi NC 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) = jacobiNC(u,m); fcontour(f,'Fill','on') title('Jacobi NC 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 NC Elliptic Function

The Jacobi NC elliptic function is

nc(u,m) = 1/cn(u,m)

where cn 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

Symbolic Math Toolbox Documentation

Mathematical Modeling with Symbolic Math Toolbox

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