## Fox's H-Function

A very general function defined by

where , , , and are Complex Numbers such that the pole of for , 2, ..., coincides with any Pole of for , 2, ..., . In addition , is a Contour in the complex -plane from to such that and lie to the right and left of , respectively.

Carter, B. D. and Springer, M. D. The Distribution of Products, Quotients, and Powers of Independent -Functions.'' SIAM J. Appl. Math. 33, 542-558, 1977.
Fox, C. The and -Functions as Symmetrical Fourier Kernels.'' Trans. Amer. Math. Soc. 98, 395-429, 1961.