The subject of special functions is often presented as a collection of disparate results, which are rarely organised in a coherent way. This book answers the need for a different approach to the subject. The authors' main goals are to emphasise general unifying principles coherently and to provide clear motivation, efficient proofs, and original references for all of the principal results. The book covers standard material, but also much more, including chapters on discrete orthogonal polynomials and elliptic functions. The authors show how a very large part of the subject traces back to two equations – the hypergeometric equation and the confluent hypergeometric equation – and describe the various ways in which these equations are canonical and special. Providing ready access to theory and formulas, this book serves as an ideal graduate-level textbook as well as a convenient reference.

About the Authors

Richard Beals is Professor Emeritus of Mathematics at Yale University.

Roderick Wong is Professor of Mathematics and Vice President for Research at the City University of Hong Kong.

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