An infinite family of Engel expansions of Rogers-Ramanujan type

DOI10.1006/aama.2000.0686zbMath0972.11068OpenAlexW2053233439MaRDI QIDQ1585499

Arnold Knopfmacher, George E. Andrews, Paule, Peter

Publication date: 16 November 2000

Published in: Advances in Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/aama.2000.0686

zbMATH Keywords

Rogers-Ramanujan identitiesextended Engel expansion

Mathematics Subject Classification ID

(q)-calculus and related topics (05A30) Combinatorial aspects of partitions of integers (05A17) Metric theory of other algorithms and expansions; measure and Hausdorff dimension (11K55) Elementary theory of partitions (11P81) Basic orthogonal polynomials and functions (Askey-Wilson polynomials, etc.) (33D45)

Related Items (11)

Nevanlinna extremal measures for polynomials related to \(q^{-1}\)-Fibonacci polynomials ⋮ q-ENGEL SERIES EXPANSIONS AND SLATER'S IDENTITIES ⋮ Unnamed Item ⋮ SumCracker: A package for manipulating symbolic sums and related objects ⋮ Polynomial solution of quantum Grassmann matrices ⋮ Continued fraction proofs of \(m\)-versions of some identities of Rogers-Ramanujan-Slater type ⋮ One-parameter generalizations of Rogers-Ramanujan type identities ⋮ Engel Series Expansions of Laurent Series and Hausdorff Dimensions ⋮ A Mathematica package for \(q\)-holonomic sequences and power series ⋮ On Jackson’s proof of Ramanujan’s 1ψ1 summation formula ⋮ Partial-sum analogues of the Rogers-Ramanujan identities

Cites Work

• Inverse polynomial expansions of Laurent series
• 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
• Variants of the Rogers-Ramanujan identities
• Engel expansions and the Rogers-Ramanujan identities
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