Basic hypergeometric series
著者
書誌事項
Basic hypergeometric series
（Encyclopedia of mathematics and its applications / edited by G.-C. Rota, v. 96）
Cambridge University Press, 2004
2nd ed
- : hbk
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注記
Bibliography: p. 367-414
Includes indexes
内容説明・目次
内容説明
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.
目次
- Foreword
- Preface
- 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 Askey-Wilson q-beta integral and some associated formulas
- 7. Applications to orthogonal polynomials
- 8. Further applications
- 9. Linear and bilinear generating functions for basic orthogonal polynomials
- 10. q-series in two or more variables
- 11. Elliptic, modular, and theta hypergeometric series
- Appendices
- References
- Author index
- Subject index
- Symbol index.
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