Function Repository Resource:

# KurepaK

Evaluate the Kurepa function

Contributed by: Jan Mangaldan
 ResourceFunction["KurepaK"][z] gives the Kurepa function K(z).

## Details

Mathematical function, suitable for both symbolic and numerical manipulation.
The Kurepa function is also known as the left factorial.
The Kurepa function is defined as for positive integers n and is defined through analytic continuation elsewhere.
For integer arguments, ResourceFunction["KurepaK"] automatically evaluates to exact values.
ResourceFunction["KurepaK"] can be evaluated to arbitrary numerical precision.

## Examples

### Basic Examples (3)

Evaluate numerically:

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Plot over a subset of the reals:

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Series expansion at the origin:

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### Scope (3)

Evaluate for complex arguments:

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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 (2)

A functional equation satisfied by KurepaK:

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Compare KurepaK with its integral representation:

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## Version History

• 1.0.0 – 08 March 2021