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:

 In:= Out= Expand in terms of generalized hypergeometric functions:

 In:= Out= Verify that the two expressions are equivalent:

 In:= Out= ### Scope (2)

A generalized Meijer G-function:

 In:= Out= Generate the hypergeometric representation:

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

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

 In:= Out= Wrap the HypergeometricPFQ heads in Inactive to prevent evaluation:

 In:= Out= ### Properties and Relations (3)

FunctionExpand always tries to convert to simpler functions whenever possible:

 In:= Out= MeijerGToHypergeometricPFQ performs a less drastic conversion:

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

 In:= Out= ### Possible Issues (3)

MeijerG expressions that autoevaluate cannot be directly converted:

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

 In:= Out= Use Activate to see the simpler expression:

 In:= Out= Piecewise results can be returned in some cases:

 In:= Out= Logarithmic cases will not be converted:

 In:= Out= ## Version History

• 1.0.0 – 23 March 2021