q-series : their development and application in analysis, number theory, combinatorics, physics, and computer algebra
著者
書誌事項
q-series : their development and application in analysis, number theory, combinatorics, physics, and computer algebra
（Regional conference series in mathematics, no. 66）
Published for the Conference Board of the Mathematical Sciences by the American Mathematical Society, c1986
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注記
Bibliography: p. 117-130
内容説明・目次
内容説明
This book integrates recent developments and related applications in $q$-series with a historical development of the field, focusing on major breakthroughs and the author's own research interests. The author develops both the important analytic topics (Bailey chains, integrals, and constant terms) and applications to additive number theory. He concludes with applications to physics and computer algebra and a section on results closely related to Ramanujan's ""Lost Notebook."" With its wide range of applications, the book will interest researchers and students in combinatorics, additive number theory, special functions, statistical mechanics, and computer algebra. It is understandable to even a beginning graduate student in mathematics who has a background in advanced calculus and some mathematical maturity.
目次
Found opportunities Classical special functions and L. J. Rogers W. N. Bailey's extension of Roger's work Constant terms Integrals Partitions and $q$-series Partitions and constant terms The hard hexagon model Ramanujan Computer algebra Appendix A. W. Gosper's Proof that $\lim_{q\rightarrow 1^-}\Gamma_q(x)=\Gamma (x)$ Appendix B. Roger's symmetric expansion of $\psi (\lambda, \mu,\nu, q, \theta)$ Appendix C. Ismail's proof of the $_1\psi_1$-summation and Jocobi's triple product identity References.
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