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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
$q$-Series: Their Development and Application in Analysis, Number Theory, Combinatorics, Physics and Computer Algebra
Softcover ISBN:  978-0-8218-0716-3
Product Code:  CBMS/66
List Price: $28.00
Individual Price: $22.40
eBook ISBN:  978-1-4704-2426-8
Product Code:  CBMS/66.E
List Price: $26.00
Individual Price: $20.80
Softcover ISBN:  978-0-8218-0716-3
eBook: ISBN:  978-1-4704-2426-8
Product Code:  CBMS/66.B
List Price: $54.00 $41.00
$q$-Series: Their Development and Application in Analysis, Number Theory, Combinatorics, Physics and Computer Algebra
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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
Softcover ISBN:  978-0-8218-0716-3
Product Code:  CBMS/66
List Price: $28.00
Individual Price: $22.40
eBook ISBN:  978-1-4704-2426-8
Product Code:  CBMS/66.E
List Price: $26.00
Individual Price: $20.80
Softcover ISBN:  978-0-8218-0716-3
eBook ISBN:  978-1-4704-2426-8
Product Code:  CBMS/66.B
List Price: $54.00 $41.00
  • Book Details
     
     
    CBMS Regional Conference Series in Mathematics
    Volume: 661986; 130 pp
    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.

    Readership

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

  • Table of Contents
     
     
    • 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
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Accessibility – to request an alternate format of an AMS title
Volume: 661986; 130 pp
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.

Readership

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
Review Copy – for publishers of book reviews
Accessibility – to request an alternate format of an AMS title
Please select which format for which you are requesting permissions.