In mathematics, the Fox H-function is a generalization of the Meijer G-function and the Fox–Wright function introduced by . It is defined by the Mellin–Barnes integral
where L is a certain contour separating the poles of the two factors in the numerator.
Relation to other functions
Meijer G-function Compare to the Meijer G-function
The special case for which the Fox H reduces to the Meijer G is Aj = Bk = C, C > 0 for j = 1...p and k = 1...q :
Lambert W-function A relation of the Fox H-Function to the -1 branch of the Lambert W-function is given by
where is the complex conjugate of .
Generalizations
A generalization of the Fox H-function was given by Ram Kishore Saxena. A further generalization of this function, useful in physics and statistics, was provided by A.M. Mathai and Ram Kishore Saxena.
References
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External links hypergeom on GitLab Use in solving on MathOverflow