In mathematics, the Fox H-function H(x) is a generalization of the Meijer G-function and the FoxâÂÂWright function introduced by . It is defined by a MellinâÂÂBarnes integral
where L is a certain contour separating the poles of the two factors in the numerator.
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 .
Compare to the Meijer G-function
The special case for which the Fox H reduces to the Meijer G is A<sub>j</sub> = B<sub>k</sub> = 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.