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 :[2]
A generalization of the Fox H-function is given by Ram Kishore Saxena.[3][4] For a further generalization of this function, useful in physics and statistics was given by A.M.Mathai and Ram Kishore Saxena,[5][6]
Innayat-Hussain, AA (1987a), "New properties of hypergeometric series derivable from Feynman integrals. I: Transformation and reduction formulae", J. Phys. A: Math. Gen., 20 (13): 4109–4117, Bibcode:1987JPhA...20.4109I, doi:10.1088/0305-4470/20/13/019
Innayat-Hussain, AA (1987b), "New properties of hypergeometric series derivable from Feynman integrals. II: A generalization of the H-function", J. Phys. A: Math. Gen., 20 (13): 4119–4128, Bibcode:1987JPhA...20.4119I, doi:10.1088/0305-4470/20/13/020
Kilbas, Anatoly A. (2004), H-Transforms: Theory and Applications, CRC Press, ISBN978-0415299169
Mathai, A. M.; Saxena, Ram Kishore (1978), The H-function with applications in statistics and other disciplines, Halsted Press [John Wiley & Sons], New York-London-Sidney, ISBN978-0-470-26380-8, MR0513025