attempts to reduce expr to a single FoxH object as a function of x.
Details and Options
- FoxH representations of mathematical functions are widely used in the areas of symbolic integration, integral transforms, statistics and others.
- FoxHReduce will attempt to represent any expression as a FoxH object.
- FoxHReduce returns results in an inert form Inactive[FoxH][…].
- The original function can be recovered from the result by using Activate. »
- FoxHReduce automatically threads over lists.
- Assumptions on parameters may be specified using the Assumptions option.
- FoxHReduce has properties similar to MeijerGReduce, but it is able to generate a FoxH representation for different functions not representable in terms of MeijerGReduce.
Examplesopen allclose all
Basic Examples (2)
Elementary Functions (6)
Represent rational functions in terms of the FoxH function:
Represent algebraic functions in terms of the FoxH function:
Represent trigonometric functions and their combinations in terms of the FoxH function:
Represent hyperbolic functions and their combinations in terms of the FoxH function:
Represent exponential and logarithmic functions in terms of the FoxH function:
Represent inverse trigonometric and hyperbolic functions in terms of the FoxH function:
Special Functions (5)
Piecewise Functions (3)
Expressions involving UnitStep:
Combinations of Special Functions (2)
Products of elementary functions:
Representation for ExpIntegralEi with a monomial argument:
FoxHReduce returns a ConditionalExpression for this example:
Use Assumptions to restrict conditions on the parameter:
FoxHReduce outputs the most general representation of special functions in terms of FoxH functions:
The family of MittagLefflerE functions is FoxH representable:
However, these functions are not representable in terms of MeijerG:
For some families of special functions, the FoxH representation is simpler than the MeijerG one:
In this case, MeijerGReduce generates a rather complicated output with two MeijerG functions:
While representation via FoxHReduce is much more simpler:
For certain families, the FoxH representation is more intuitive than the MeijerG representation:
Properties & Relations (6)
FoxHReduce returns FoxH representation of the function in Inactive form:
Use Activate to evaluate the result:
FoxHReduce maps over sums and products:
FoxHReduce takes lists and matrices as arguments:
FoxHReduce may be regarded as the inverse of FoxH:
FoxHReduce may generate a ConditionalExpression:
FoxHReduce may take an Inactive MeijerG as an input:
Possible Issues (1)
Some advanced special functions are not represented in terms of FoxH:
Neat Examples (1)
Create a gallery of FoxH representations for a set of elementary and special functions:
Wolfram Research (2021), FoxHReduce, Wolfram Language function, https://reference.wolfram.com/language/ref/FoxHReduce.html.
Wolfram Language. 2021. "FoxHReduce." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/FoxHReduce.html.
Wolfram Language. (2021). FoxHReduce. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/FoxHReduce.html