is the Fox H-function .
- Mathematical function, suitable for both symbolic and numerical manipulation.
- FoxH generalizes the MeijerG function and is defined by the Mellin–Barnes integral where and are positive real numbers and the integration is along a path separating the poles of from the poles of .
- Three choices are possible for the path :
a. is a loop beginning at and ending at and encircling all the poles of once in the positive direction.
b. is a loop beginning at and ending at and encircling all the poles of once in the negative direction.
c. is a contour starting at the point and going to such that all the poles of are separated from the poles of .
- FoxH specializes to MeijerG if for and : .
- In many special cases, FoxH is automatically converted to other functions.
- FoxH can be evaluated for arbitrary complex parameters.
- FoxH can be evaluated to arbitrary numerical precision.
- FoxH automatically threads over lists.
Examplesopen allclose all
Basic Examples (6)
Numerical Evaluation (5)
Specific Values (3)
Evaluate FoxH symbolically:
Function Properties (5)
Formula for the derivative of a specific FoxH with respect to z:
Compute the indefinite integral using Integrate:
Series Expansions (4)
Get the series expansion of some FoxH function at the origin:
The first three approximations of this FoxH function around :
Find the series expansion of a general FoxH function at the origin:
Get the general term in the series expansion using SeriesCoefficient:
A root of the trinomial equation can be written in terms of FoxH:
The roots of the general trinomial can also be expressed in terms of FoxH:
Properties & Relations (2)
Possible Issues (3)
Neat Examples (1)
Many elementary and special functions are special cases of FoxH:
Wolfram Research (2021), FoxH, Wolfram Language function, https://reference.wolfram.com/language/ref/FoxH.html (updated 2021).
Wolfram Language. 2021. "FoxH." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2021. https://reference.wolfram.com/language/ref/FoxH.html.
Wolfram Language. (2021). FoxH. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/FoxH.html