Rogers-Ramanujan computer searches

DOI10.1016/j.jsc.2009.02.003zbMath1175.33018arXiv1812.08222OpenAlexW2151228973MaRDI QIDQ1023270

Peter Zimmer, Andrew V. Sills, James Mc Laughlin

Publication date: 11 June 2009

Published in: Journal of Symbolic Computation (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1812.08222

zbMATH Keywords

\(q\)-seriesRogers-Ramanujan identitiesBailey pairs\(q\)-Zeilberger algorithmfalse theta functions\(q\)-WZ certification

Mathematics Subject Classification ID

Binomial coefficients; factorials; (q)-identities (11B65) Basic hypergeometric functions in one variable, ({}_rphi_s) (33D15) Symbolic computation of special functions (Gosper and Zeilberger algorithms, etc.) (33F10) Partition identities; identities of Rogers-Ramanujan type (11P84)

Related Items (8)

IdentityFinder and Some New Identities of Rogers–Ramanujan Type ⋮ On a pair of identities from Ramanujan's lost notebook ⋮ Rogers-Ramanujan type identities via Abel's lemma on summation by parts ⋮ On some continued fraction expansions of the Rogers-Ramanujan type ⋮ A 𝑞-series identity via the 𝔰𝔩₃ colored Jones polynomials for the (2,2𝔪)-torus link ⋮ One-parameter generalizations of Rogers-Ramanujan type identities ⋮ Bilateral Bailey lemma and Rogers-Ramanujan identities ⋮ A variant of \texttt{IdentityFinder} and some new identities of Rogers-Ramanujan-MacMahon type

Uses Software

• Engel
• Maple
• Mathematica
• PARI/GP
• qZeil
• RRtools
• qseries

Cites Work

• Multiple series Rogers-Ramanujan type identities
• An algorithmic proof theory for hypergeometric (ordinary and ``\(q\)) multisum/integral identities
• A fast algorithm for proving terminating hypergeometric identities
• A purely verification proof of the first Rogers-Ramanujan identity
• Ramanujan-Slater type identities related to the moduli 18 and 24
• Some more identities of the Rogers-Ramanujan type
• Lattice gas generalization of the hard hexagon model. III: \(q\)-trinomial coefficients
• The method of creative telescoping
• On Zeilberger's algorithm and its \(q\)-analogue
• Short and easy computer proofs of the Rogers-Ramanujan identities and of identities of similar type
• An algorithmic approach to discovering and proving \(q\)-series identities
• Finite Rogers-Ramanujan type identities
• Engel expansions and the Rogers-Ramanujan identities
• Rogers-Ramanujan-Slater type identities
• \texttt{RRtools} -- a Maple package for aiding the discovery and proof of finite Rogers-Ramanujan type identities
• Rational Functions Certify Combinatorial Identities
• Combinatorics of Ramanujan–Slater Type Identities
• Applications of q-Lagrange Inversion to Basic Hypergeometric Series
• A Computer-Assisted Investigation of Ramanujan Pairs
• Special values of the dilogarithm function
• q-ENGEL SERIES EXPANSIONS AND SLATER'S IDENTITIES
• Partition theorems related to the Rogers-Ramanujan identities
• Identities of the Rogers-Ramanujan Type
• Some Identities in Combinatory Analysis
• On the Simplification of Some Identities of the Rogers-Ramanujan Type
• A New Proof of Rogers's Transformations of Infinite Series
• Further Identities of the Rogers-Ramanujan Type
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