Function Repository Resource:

# NielsenG

Evaluate the Nielsen function G

Contributed by: Jan Mangaldan
 ResourceFunction["NielsenG"][z] gives the Nielsen function g(z).

## Details

Mathematical function, suitable for both symbolic and numerical manipulation.
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ResourceFunction["NielsenG"][z] has a branch cut discontinuity in the complex z plane running from - to 0.
For certain special arguments, ResourceFunction["NielsenG"] automatically evaluates to exact values.
ResourceFunction["NielsenG"] 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 (4)

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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Simple exact values are generated automatically:

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### Applications (1)

Plot the logarithm of the absolute value in the complex plane:

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### Properties and Relations (3)

Express CosIntegral and SinIntegral in terms of NielsenF and NielsenG:

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NielsenG is the Laplace transform of :

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A representation of NielsenG in terms of MeijerG:

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### Possible Issues (3)

NielsenG is automatically expanded in terms of CosIntegral and SinIntegral:

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Plugging in a large complex argument after expansion leads to inaccurate numerical results:

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Evaluate the function directly:

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## Version History

• 1.0.0 – 10 March 2021