Variants of the Rogers-Ramanujan identities

DOI10.1006/aama.1999.0658zbMath0944.33015OpenAlexW1977204800MaRDI QIDQ1970525

Mourad E. H. Ismail, Dennis W. Stanton, Kristina C. Garrett

Publication date: 15 September 2000

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

Full work available at URL: https://doi.org/10.1006/aama.1999.0658

zbMATH Keywords

Rogers-Ramanujan identities\(q\)-ultraspherical polynomials

Mathematics Subject Classification ID

Combinatorial aspects of partitions of integers (05A17) Elementary theory of partitions (11P81) Basic orthogonal polynomials and functions (Askey-Wilson polynomials, etc.) (33D45)

Related Items (44)

Neighborly partitions and the numerators of Rogers–Ramanujan identities ⋮ Integral and series representations of q-polynomials and functions: Part III theta, Ramanujan and q-Bessel functions ⋮ Partition bijections, a survey ⋮ On the families of polynomials forming a part of the Askey–Wilson scheme and their probabilistic applications ⋮ Refinements of the Rogers–Ramanujan Identities ⋮ Several new product identities in relation to Rogers-Ramanujan type sums and mock theta functions ⋮ 𝑞-Bessel functions and Rogers-Ramanujan type identities ⋮ On the growth of Artin-Tits monoids and the partial theta function ⋮ On some 2𝐷 orthogonal 𝑞-polynomials ⋮ Bilateral identities of the Rogers–Ramanujan type ⋮ Bootstrapping and Askey-Wilson polynomials ⋮ Shifted versions of the Bailey and well-poised Bailey lemmas ⋮ A weighted extension of Fibonacci numbers ⋮ Interview with Helmut Prodinger ⋮ A multilateral Bailey lemma and multiple Andrews-Gordon identities ⋮ Some new identities of Rogers-Ramanujan type ⋮ New companions to the Andrews-Gordon identities motivated by commutative algebra ⋮ Two generalizations of Jacobi's triple product identity and their applications ⋮ Superconformal index, BPS monodromy and chiral algebras ⋮ Rogers-Ramanujan type identities and nil-DAHA ⋮ Spectral analysis of two doubly infinite Jacobi matrices with exponential entries ⋮ An elliptic $BC_n$ Bailey Lemma, multiple Rogers–Ramanujan identities and Euler’s Pentagonal Number Theorems ⋮ Dyson's new symmetry and generalized Rogers-Ramanujan identities ⋮ Mahonian pairs ⋮ Polynomial solution of quantum Grassmann matrices ⋮ Overpartitions into distinct parts without short sequences ⋮ Continued fraction proofs of \(m\)-versions of some identities of Rogers-Ramanujan-Slater type ⋮ Expansions of one density via polynomials orthogonal with respect to the other ⋮ Multiple analogues of binomial coefficients and families of related special numbers ⋮ One-parameter generalizations of Rogers-Ramanujan type identities ⋮ A combinatorial proof of the Rogers--Ramanujan and Schur identities ⋮ Tribasic integrals and identities of Rogers-Ramanujan type ⋮ Arithmetic properties of \(q\)-Fibonacci numbers and \(q\)-Pell numbers ⋮ A framework of Rogers-Ramanujan identities and their arithmetic properties ⋮ Bilateral Bailey lemma and Rogers-Ramanujan identities ⋮ Asymptotics of partition functions in a fermionic matrix model and of related q‐polynomials ⋮ On a Ramanujan type entire function and its zeros ⋮ Connection relations for \(q\)-Taylor polynomial bases ⋮ A Bailey type identity with applications related to integer representations ⋮ Two expansion formulas involving the Rogers–Szegő polynomials with applications ⋮ An infinite family of Engel expansions of Rogers-Ramanujan type ⋮ On Jackson’s proof of Ramanujan’s 1ψ1 summation formula ⋮ Partial-sum analogues of the Rogers-Ramanujan identities ⋮ Integral and series representations of 𝑞-polynomials and functions: Part II Schur polynomials and the Rogers-Ramanujan identities

Cites Work

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• Orthogonal polynomials associated with the Rogers-Ramanujan continued fraction
• Multiple series Rogers-Ramanujan type identities
• An easy proof of the Rogers-Ramanujan identities
• The combinatorics of q-Hermite polynomials and the Askey-Wilson integral
• The Rogers-Ramanujan identities without Jacobi's triple product
• A Rogers-Ramanujan bijection
• An injection for the Ehrenpreis Rogers-Ramanujan problem
• Some formulas related to the Rogers-Ramanujan identities
• Some basic hypergeometric orthogonal polynomials that generalize Jacobi polynomials
• Method for constructing bijections for classical partition identities
• On Partitions, Orthogonal Polynomials and the Expansion of Certain Infinite Products
• A Motivated Proof of the Rogers-Ramanujan Identities
• Change of base in Bailey pairs

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