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9781470456238 Academic Inspection Copy

An Introduction to Q-analysis

  • ISBN-13: 9781470456238
  • Publisher: AMERICAN MATHEMATICAL SOCIETY
    Imprint: AMERICAN MATHEMATICAL SOCIETY
  • By Warren P. Johnson
  • Price: AUD $181.00
  • Stock: 0 in stock
  • Availability: This book is temporarily out of stock, order will be despatched as soon as fresh stock is received.
  • Local release date: 30/04/2021
  • Format: Paperback 519 pages Weight: 945g
  • Categories: Mathematics [PB]
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Starting from simple generalizations of factorials and binomial coefficients, this book gives a friendly and accessible introduction to $q$-analysis, a subject consisting primarily of identities between certain kinds of series and products. Many applications of these identities to combinatorics and number theory are developed in detail. There are numerous exercises to help students appreciate the beauty and power of the ideas, and the history of the subject is kept consistently in view. The book has few prerequisites beyond calculus. It is well suited to a capstone course, or for self-study in combinatorics or classical analysis. Ph.D. students and research mathematicians will also find it useful as a reference.
Warren P. Johnson, Connecticut College, New London, CT, USA
Inversions $q$-binomial theorems Partitions I: Elementary theory Partitions II: Geometry theory More $q$-identites: Jacobi, Guass, and Heine Ramanujan's $_1\psi_1$ summation formula Sums of squares Ramanujan's congruences Some combinatorial results The Rogers-Ramanujan identities I: Schur The Rogers-Ramanujan identities II: Rogers The Rogers-Selberg function Bailey's $_6\psi_6$ sum A brief guide to notation Infinite products Tannery's theorem Bibliography Index of names Index of topics
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