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)

UnitStep:

UnitBox:

Expressions involving UnitStep:

ConditionalExpression:

General Functions  (4)

Products of elementary functions:

Product of exponential and Airy functions:

Products involving Bessel functions:

Representation for ExpIntegralEi with a monomial argument:

SinIntegral:

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 int_0^infty(z+1)^(-3/2) TemplateBox[{{-, z}}, EllipticK]dz:

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: 22-December-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: 22-December-2024 ]}