Basic Hypergeometric Series
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.
What people are saying - Write a review
We haven't found any reviews in the usual places.
1 Basic hypergeometric series
2 Summation transformation and expansion formulas
3 Additional summation transformation and expansion formulas
4 Basic contour integrals
5 Bilateral basic hypergeometric series
6 The AskeyWilson qbeta integral and some associated formulas
7 Applications to orthogonal polynomials
8 Further applications
11 Elliptic modular and theta hypergeometric series
Appendix I Identities involving qshifted factorials qgamma functions and qbinomial coefficients ...
Appendix II Selected summation formulas
Appendix III Selected transformation formulas
9 Linear and bilinear generating functions for basic orthogonal polynomials
10 qseries in two or more variables
Other editions - View all
abcd Agarwal Al-Salam analytic continuation Andrews aq/b aq/bc aq/bd aq/c aq/d aq/e aq/f Askey and Wilson Askey-Wilson polynomials Bailey Bailey’s balancing condition basic hypergeometric series bibasic bq/a Chihara Clausen’s coefficients complex numbers contour integral converges deﬁned derived elliptic analogue equation expansion formula extension ﬁnd ﬁrst follows Frenkel and Turaev Gasper and Rahman Gauss hence idem identity integer integral representation Ismail Jackson Koornwinder left side Math modular nonnegative integers nonterminating notation obtain orthogonal polynomials orthogonality relation parameters Poisson kernel product formula proof Prove q-analogue q-binomial theorem q-derivative q-exponential q-gamma function q-integral q-Jacobi polynomials q-series q-shifted factorials q)oO quadratic transformation recurrence relation replace right side Rosengren Show Spiridonov Stanton summation formula Suslov terminating transformation formula Verma very-well-poised VWP-balanced Warnaar well-poised zero