Function Repository Resource:

# StruveKelvinStei

Evaluate the Struve–Kelvin stei function

Contributed by: Jan Mangaldan
 ResourceFunction["StruveKelvinStei"][z] gives the Struve–Kelvin function stei(z). ResourceFunction["StruveKelvinStei"][n,z] gives the Struve–Kelvin function stein(z).

## Details

Mathematical function, suitable for both symbolic and numerical manipulation.
For positive real values of parameters, stein(z)= Im(Hn(ze3πi/4)), where H is the StruveH function. For other values, stei is defined by analytic continuation.
ResourceFunction["StruveKelvinStei"][n,z] has a branch cut discontinuity in the complex z plane running from - to 0.
ResourceFunction["StruveKelvinStei"][z] is equivalent to ResourceFunction["StruveKelvinStei"][0,z].
For certain special arguments, ResourceFunction["StruveKelvinStei"] automatically evaluates to exact values.
ResourceFunction["StruveKelvinStei"] can be evaluated to arbitrary numerical precision.

## Examples

### Basic Examples (2)

Evaluate numerically:

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Plot stei(x):

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### Scope (4)

Evaluate for complex arguments and orders:

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Evaluate to high precision:

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The precision of the output tracks the precision of the input:

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### Properties and Relations (1)

Use FunctionExpand to expand Struve–Kelvin functions of half-integer orders:

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## Version History

• 1.0.0 – 04 March 2021