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Special Functions


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Table of Contents

1. The Gamma and Beta functions; 2. The hypergeometric functions; 3. Hypergeometric transformations and identities; 4. Bessel functions and confluent hypergeometric functions; 5. Orthogonal polynomials; 6. Special orthogonal transformations; 7. Topics in orthogonal polynomials; 8. The Selberg integral and its applications; 9. Spherical harmonics; 10. Introduction to q-series; 11. Partitions; 12. Bailey chains; Appendix 1. Infinite products; Appendix 2. Summability and fractional integration; Appendix 3. Asymptotic expansions; Appendix 4. Euler-Maclaurin summation formula; Appendix 5. Lagrange inversion formula; Appendix 6. Series solutions of differential equations.

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An overview of special functions, focusing on the hypergeometric functions and the associated hypergeometric series.


'Occasionally there is published a mathematics book that one is compelled to describe as, well, let us say, special. Special Functions is certainly one of those rare books. ... this treatise ... should become a classic. Every student, user, and researcher in analysis will want to have it close at hand as she/he works.' The Mathematical Intelligencer ' ... the material is written in an excellent manner ... I recommend this book warmly as a rich source of information to everybody who is interested in 'Special Functions'.' Zentralblatt MATH ' ... this book contains a wealth of fascinating material which is presented in a user-friendly way. If you want to extend your knowledge of special functions, this is a good place to start. Even if your interests are in number theory or combinatorics, there is something for you too ... the book can be warmly recommended and should be in all good libraries.' Adam McBride, The Mathematical Gazette ' ... it comes into the range of affordable books that you want to (and probably should have on your desk'. Jean Mawhin, Bulletin of the Belgian Mathematical Society 'The book is full of beautiful and interesting formulae, as was always the case with mathematics centred around special functions. It is written in the spirit of the old masters, with mathemtics developed in terms of formulas. There are many historical comments in the book. It can be recommended as a very useful reference.' European Mathematical Society '... full of beautiful and interesting formulae ... It can be recommended as a very useful reference.' EMS Newsletter

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