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$q$-Series: Their Development and Application in Analysis, Number Theory, Combinatorics, Physics and Computer Algebra

G. Andrews Pennsylvania State University, University Park, PA
A co-publication of the AMS and CBMS
Available Formats:
Softcover ISBN: 978-0-8218-0716-3
Product Code: CBMS/66
130 pp
List Price: $26.00 Individual Price:$20.80
Electronic ISBN: 978-1-4704-2426-8
Product Code: CBMS/66.E
130 pp
List Price: $24.00 Individual Price:$19.20
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This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.
List Price: $39.00 Click above image for expanded view$q$-Series: Their Development and Application in Analysis, Number Theory, Combinatorics, Physics and Computer Algebra G. Andrews Pennsylvania State University, University Park, PA A co-publication of the AMS and CBMS Available Formats:  Softcover ISBN: 978-0-8218-0716-3 Product Code: CBMS/66 130 pp  List Price:$26.00 Individual Price: $20.80  Electronic ISBN: 978-1-4704-2426-8 Product Code: CBMS/66.E 130 pp  List Price:$24.00 Individual Price: $19.20 Bundle Print and Electronic Formats and Save! This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version. List Price:$39.00
• Book Details

CBMS Regional Conference Series in Mathematics
Volume: 661986
MSC: Primary 11; Secondary 05; 33; 68; 82;

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.

Researchers and students in combinatorics, additive number theory, special functions, statistical mechanics, and computer algebra.

• Chapters
• Chapter 1. Found Opportunities
• Chapter 2. Classical Special Functions and L. J. Rogers
• Chapter 3. W. N. Bailey’s Extension of Rogers’s Work
• Chapter 4. Constant Terms
• Chapter 5. Integrals
• Chapter 6. Partitions and $q$-Series
• Chapter 7. Partitions and Constant Terms
• Chapter 8. The Hard Hexagon Model
• Chapter 9. Ramanujan
• Chapter 10. Computer Algebra
• Appendix A. W. Gosper’s Proof that $\lim _{q \to 1^{-}}\Gamma _q(x) = \Gamma (x)$
• Appendix B. Rogers’s Symmetric Expansion of $\psi (\lambda , \mu , \nu , q, \theta )$
• Appendix C. Ismail’s Proof of the $_1\psi _1$-Summation and Jacobi’s Triple Product Identity
• Request Review Copy
Volume: 661986
MSC: Primary 11; Secondary 05; 33; 68; 82;

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.

Researchers and students in combinatorics, additive number theory, special functions, statistical mechanics, and computer algebra.

• Chapters
• Chapter 1. Found Opportunities
• Chapter 2. Classical Special Functions and L. J. Rogers
• Chapter 3. W. N. Bailey’s Extension of Rogers’s Work
• Chapter 4. Constant Terms
• Chapter 5. Integrals
• Chapter 6. Partitions and $q$-Series
• Chapter 7. Partitions and Constant Terms
• Chapter 8. The Hard Hexagon Model
• Chapter 9. Ramanujan
• Chapter 10. Computer Algebra
• Appendix A. W. Gosper’s Proof that $\lim _{q \to 1^{-}}\Gamma _q(x) = \Gamma (x)$
• Appendix B. Rogers’s Symmetric Expansion of $\psi (\lambda , \mu , \nu , q, \theta )$
• Appendix C. Ismail’s Proof of the $_1\psi _1$-Summation and Jacobi’s Triple Product Identity
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