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.
Examplesopen allclose all
Basic Examples (2)
Elementary Functions (6)
Special Functions (5)
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:
MeijerGReduce returns a ConditionalExpression for this example:
Use Assumptions to restrict conditions on the parameter:
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:
Neat Examples (1)
Create a gallery of MeijerG representations:
Wolfram Research (2016), MeijerGReduce, Wolfram Language function, https://reference.wolfram.com/language/ref/MeijerGReduce.html.
Wolfram Language. 2016. "MeijerGReduce." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/MeijerGReduce.html.
Wolfram Language. (2016). MeijerGReduce. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/MeijerGReduce.html