Basic Hypergeometric Series

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Cambridge University Press, Oct 4, 2004 - Mathematics - 428 pages
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This revised and expanded new edition will continue to meet the needs for an authoritative, up-to-date, self contained, and comprehensive account of the rapidly growing field of basic hypergeometric series, or q-series. Simplicity, clarity, deductive proofs, thoughtfully designed exercises, and useful appendices are among its strengths. The first five chapters cover basic hypergeometric series and integrals, whilst the next five are devoted to applications in various areas including Askey-Wilson integrals and orthogonal polynomials, partitions in number theory, multiple series, orthogonal polynomials in several variables, and generating functions. Chapters 9-11 are new for the second edition, the final chapter containing a simplified version of the main elements of the theta and elliptic hypergeometric series as a natural extension of the single-base q-series. Some sections and exercises have been added to reflect recent developments, and the Bibliography has been revised to maintain its comprehensiveness.
 

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Contents

1 Basic hypergeometric series
1
2 Summation transformation and expansion formulas
38
3 Additional summation transformation and expansion formulas
69
4 Basic contour integrals
113
5 Bilateral basic hypergeometric series
137
6 The AskeyWilson qbeta integral and some associated formulas
154
7 Applications to orthogonal polynomials
175
8 Further applications
217
11 Elliptic modular and theta hypergeometric series
302
Appendix I Identities involving qshifted factorials qgamma functions and qbinomial coefficients ...
351
Appendix II Selected summation formulas
354
Appendix III Selected transformation formulas
359
References
367
Symbol index
415
Author index
418
Subject index
423

9 Linear and bilinear generating functions for basic orthogonal polynomials
259
10 qseries in two or more variables
282

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