A Tribute to Richard Askey, and an Expansive View of Some of his Favorite Beta Integrals

This article represents a personal tribute to Richard Askey together with a new look at some of his favorite integrals, including the Cauchy beta integral. The article also provides some new multidimensional extensions of Cauchy’s beta integral in which the domain of integration is the space of real symmetric matrices, and these multidimensional integrals are used to obtain some special cases of the Cauchy–Selberg integrals.