Fox H-function

Summary

The Fox H-function is a generalisation of the Meijer G-function. In its Barnes integral the gamma factors may have the form $\Gamma(b + B s)$ with a positive scale $B$, not only $\Gamma(b + s)$. When all scales equal $1$, it is a Meijer G-function. The extra freedom covers functions such as the Mittag-Leffler and Fox–Wright functions. H-functions appear in fractional calculus and as densities in probability, for instance of products and quotients of independent random variables.