Basic Hypergeometric SeriesCambridge University Press, 4 oct. 2004 - 428 pages 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. |
Table des matières
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 |
415 | |
418 | |
423 | |
9 Linear and bilinear generating functions for basic orthogonal polynomials | 259 |
10 qseries in two or more variables | 282 |
Autres éditions - Tout afficher
Expressions et termes fréquents
a₁ abcd aeio Andrews aq/b aq/bc aq/c aq/cd aq/d aq/e aq/f aqn+1 ar+1 Askey Askey-Wilson polynomials b₁ Bailey balanced basic hypergeometric functions basic hypergeometric series bc/a bd/a be/a bq/a bq/c bq/d bq/e bq/f coefficients contour converges de/bc defined derived elliptic Gasper and Rahman hypergeometric functions identities Ismail Jackson Koornwinder Milne nonnegative integers obtain orthogonal polynomials orthogonality relation parameters Pn(x Poisson kernel Proc product formula proof Prove q-analogue q-binomial theorem q-exponential q-gamma function q-integral q-Jacobi polynomials q-series q)n q qn+1 quadratic transformation replace right side Rosengren Schlosser Show Spiridonov Stanton summation formula Suslov terminating theorem transformation formula Verma very-well-poised VWP-balanced Warnaar well-poised ΣΣ