Higher Transcendental Functions [Volumes I-III]

The work of which this book is the first volume might be described as an up-to-date version of Part II. The Transcendental Functions of Whittaker and Watson's celebrated "Modern Analysis". Bateman (who was a pupil of E. T. Whittaker) planned his "Guide to the Functions" on a gigantic scale. In addition to a detailed account of the properties of the most important functions, the work was to include the historic origin and definition of, the basic formulas relating to, and a bibliography for all special functions ever invented or investigated. These functions were to be catalogued and classified under twelve different \nheadings according to their definition by power series, generating functions, infinite products, repeated differentiations, indefinite integrals, definite integrals, differential equations, difference equations, functional \nequations, trigonometric series, series of orthogonal functions, or integral equations. Tables of definite integrals representing each function and numerical tables of a few new functions were to form part of the "Guide". An extensive table of definite integrals and a Guide to numerical tables of special functions were planned as companion works.