Function Repository Resource:

# MeijerGToHypergeometricPFQ

Express MeijerG expressions in terms of HypergeometricPFQ

Contributed by: Jan Mangaldan
 ResourceFunction["MeijerGToHypergeometricPFQ"][expr] converts MeijerG expressions in expr to a form involving HypergeometricPFQ. ResourceFunction["MeijerGToHypergeometricPFQ"][expr,f] wraps f around any HypergeometricPFQ head in the result.

## Details

ResourceFunction["MeijerGToHypergeometricPFQ"] uses Slater's theorem to expand out the Meijer G-function to a sum of generalized hypergeometric functions.

## Examples

### Basic Examples (3)

A Meijer G-function:

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Expand in terms of generalized hypergeometric functions:

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Verify that the two expressions are equivalent:

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### Scope (2)

A generalized Meijer G-function:

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Generate the hypergeometric representation:

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Use MeijerGReduce to convert a special function to its equivalent MeijerG representation:

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The result after conversion with MeijerGToHypergeometricPFQ does not have HypergeometricPFQ terms due to autoevaluation:

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Wrap the HypergeometricPFQ heads in Inactive to prevent evaluation:

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### Properties and Relations (3)

FunctionExpand always tries to convert to simpler functions whenever possible:

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MeijerGToHypergeometricPFQ performs a less drastic conversion:

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If Inactive is not supplied as the second argument, the resulting HypergeometricPFQ expressions might still autoevaluate:

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### Possible Issues (3)

MeijerG expressions that autoevaluate cannot be directly converted:

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Wrap MeijerG in Inactive and use Inactive as the second argument to prevent evaluation:

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Use Activate to see the simpler expression:

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Piecewise results can be returned in some cases:

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Logarithmic cases will not be converted:

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## Version History

• 1.0.0 – 23 March 2021