3 research outputs found
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
headings according to their definition by power series, generating functions,
infinite products, repeated differentiations, indefinite integrals, definite integrals, differential equations, difference equations, functional
equations, 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