MeijerGReduce

MeijerGReduce[expr,x]

attempts to reduce expr to a single MeijerG object as a function of x.

Details and Options

• MeijerG representations of mathematical functions are widely used in the areas of symbolic integration, integral transforms, statistics and others.
• MeijerGReduce will attempt to represent any expression as a MeijerG object.
• MeijerGReduce returns results in an inert form Inactive[MeijerG][].
• MeijerGReduce automatically threads over lists.
• Assumptions on parameters may be specified using the Assumptions option.

Examples

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Basic Examples(2)

Represent Sin in terms of MeijerG:

Represent BesselJ in terms of MeijerG:

Recover the original function using Activate:

Scope(18)

Elementary Functions(6)

Rational functions:

Algebraic functions:

Trigonometric functions:

Linear combination of trigonometric functions:

Hyperbolic functions:

Linear combination of hyperbolic functions:

Exponential and logarithmic functions:

Inverse trigonometric and hyperbolic functions:

Special Functions(5)

Airy functions:

Bessel functions:

Legendre functions:

Hypergeometric functions:

Elliptic functions:

Piecewise Functions(3)

Expressions involving UnitStep:

General Functions(4)

Products of elementary functions:

Product of exponential and Airy functions:

Products involving Bessel functions:

Representation for ExpIntegralEi with a monomial argument:

Options(1)

Assumptions(1)

MeijerGReduce returns a ConditionalExpression for this example:

Use Assumptions to restrict conditions on the parameter:

Applications(1)

Build a simple scheme for integration over the interval , using MeijerGReduce:

Add a rule for integrating products of inactive MeijerG expressions:

Apply the scheme to evaluate :

Obtain the same result using Integrate:

Properties & Relations(4)

MeijerGReduce returns results in Inactive form to prevent evaluation of MeijerG:

Use Activate to evaluate the result:

MeijerGReduce maps over sums and products:

MeijerGReduce may be regarded as the inverse of MeijerG:

The result from MeijerGReduce can be used in MellinTransform:

Obtain the Mellin transform directly:

Neat Examples(1)

Create a gallery of MeijerG representations:

Wolfram Research (2016), MeijerGReduce, Wolfram Language function, https://reference.wolfram.com/language/ref/MeijerGReduce.html.

Text

Wolfram Research (2016), MeijerGReduce, Wolfram Language function, https://reference.wolfram.com/language/ref/MeijerGReduce.html.

CMS

Wolfram Language. 2016. "MeijerGReduce." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/MeijerGReduce.html.

APA

Wolfram Language. (2016). MeijerGReduce. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/MeijerGReduce.html

BibTeX

@misc{reference.wolfram_2024_meijergreduce, author="Wolfram Research", title="{MeijerGReduce}", year="2016", howpublished="\url{https://reference.wolfram.com/language/ref/MeijerGReduce.html}", note=[Accessed: 09-August-2024 ]}

BibLaTeX

@online{reference.wolfram_2024_meijergreduce, organization={Wolfram Research}, title={MeijerGReduce}, year={2016}, url={https://reference.wolfram.com/language/ref/MeijerGReduce.html}, note=[Accessed: 09-August-2024 ]}