Book Review: An essay toward a unified theory of special functions

Abstract

While the familiar transcendents of mathematical physics belong to classes of functions which have been studied in various penetrating investigations of an analytic or of an algebraic character, there remain many simple formal relations which as yet seem to constitute particular properties of the particular functions, and are subsumed by no general framework. My aim is to present a theory on the basis of which some of these apparently individual formulas will easily appear as natural consequences of a few general theorems. Let us first examine some of the commonest of these relations and formulate some natural questions about them