In mathematics, the Fox H-function H(x) is a generalization of the Meijer G-function and the Fox–Wright function introduced by. It is defined by a Mellin–Barnes integral where L is a certain contour separating the poles of the two factors in the numerator.

Relation to other Functions

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 z.

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 : 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.