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(Ebook PDF) An Invitation to the Rogers Ramanujan Identities 1st Edition by Andrew Sills 1498745253 9781498745253 Full chapter

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Author(s): Sills, Andrew V
ISBN(s): 9781498745253, 1498745253
Edition: 1
File Details: PDF, 4.64 MB
Year: 2018
Language: english
SKU: EB-6837338 Category: Tags: ,

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Product details:

ISBN 10:         1498745253
ISBN 13: 978-1498745253
Author:          Andrew V. Sills

The Rogers–Ramanujan identities are a pair of infinite series―infinite product identities that were first discovered in 1894. Over the past several decades these identities, and identities of similar type, have found applications in number theory, combinatorics, Lie algebra and vertex operator algebra theory, physics (especially statistical mechanics), and computer science (especially algorithmic proof theory). Presented in a coherant and clear way, this will be the first book entirely devoted to the Rogers―Ramanujan identities and will include related historical material that is unavailable elsewhere.

 

An Invitation to the Rogers Ramanujan Identities 1st Table of contents:

1. Background and the Pre-History
1.1 Elementary Theory of Partitions
1.2 Dedekind’s Eta Function and Modular Forms
1.3 Hypergeometric Series
1.4 Wilf–Zeilberger Theory of Hypergeometric Summation
1.5 q-Analogs
1.6 Basic Hypergeometric Series
1.7 q-Binomial Theorem and Jacobi’s Triple Product Identity
1.8 q-Trinomial Coëfficients
1.9 q-Hypergeometric Transformation Formulae
1.10 Classical q-Series Identities in Two and Three Variables
1.11 Two-Variable Generating Functions

2. The Golden Age and its Modern Legacy
2.1 Hardy’s Account
2.2 Two Proofs of the Rogers–Ramanujan Identities
2.3 Rogers–Ramanujan–Bailey Machinery
2.4 Combinatorial Considerations
2.5 Close Cousins of Rogers–Ramanujan Type Identities
2.6 Enumeration

3. Infinite Families… Everywhere.
3.1 Bailey Chain
3.2 Combinatorial Generalizations of Rogers-Ramanujan Type Identities

4. Infinite to Finite
4.1 Andrews’ Method of q-Difference Equations
4.2 Reciprocal Duality
4.3 Bressoud Polynomials
4.4 Finite Ramanujan–Slater Mod 8 identities
4.5 Borwein Conjecture

5. Motivated Proofs Connections to Lie Algebras, and More Identities
5.1 “Motivated” Proofs
5.2 Connections to Lie and Vertex Operator Algebras

6. But wait… there’s more!
6.1 Partition Bijections
6.2 Rogers–Ramanujan Continued Fraction
6.3 Statistical Mechanics
6.4 Loxton’s Special Values of the Dilogarithm Function
6.5 Hall–Littlewood Polynomials
6.7 “m-Versions”
6.8 Knot Theory
6.9 Who Knows What Else?

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