An Analytic Generalization of the Rogers-Ramanujan Identities for Odd Moduli [PDF]
Proceedings of the National Academy of Sciences of the United States of America, 1974 George Andrews, Andrews George E
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New approaches of (q,k)-Fibonacci–Pell sequences via linear difference equations. Applications [PDF]
Notes on Number Theory and Discrete Mathematics, 2023 In this paper we establish some explicit formulas of (q,k)-Fibonacci–Pell sequences via linear difference equations of order 2 with variable coefficients, and explore some of their new properties. More precisely, our results are based on two approaches,
Irene Magalhães Craveiro +2 more
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Some Congruences for the Coefficients of Rogers–Ramanujan Type Identities
Mathematics, 2022 We examine a few mathematical characteristics of Rogers–Ramanujan type identities as a follow-up work. Recently authors interpreted Rogers–Ramanujan type identities combinatorially using signed color partitions.
Vasudha Gupta, Meenakshi Rana
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On relationships between q-products identities, Ralpha, Rbeta and Rm functions related to Jacobi's triple-product identity [PDF]
Mathematica Moravica, 2020 The authors establish a set of two new relationships involving q-product identities, Ralpha, Rbeta, and Rm (m = 1, 2, 3, . . .) functions; and answer a open question of Srivastava et al. [18].
Chaudhary M.P., Chaudhary Sangeeta
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Arc Spaces and Rogers-Ramanujan Identities [PDF]
Discrete Mathematics & Theoretical Computer Science, 2011 Arc spaces have been introduced in algebraic geometry as a tool to study singularities but they show strong connections with combinatorics as well. Exploiting these relations we obtain a new approach to the classical Rogers-Ramanujan Identities.
Clemens Bruschek +2 more
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Revisiting a Classic Identity That Implies the Rogers–Ramanujan Identities II
Axioms, 2021 We give a new proof of an identity due to Ramanujan. From this identity, he deduced the famous Rogers–Ramanujan identities. We prove this identity by establishing a simple recursion Jk=qkJk−1, where |q|
Hei-Chi Chan
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An extension to overpartitions of Rogers-Ramanujan identities for even moduli [PDF]
Discrete Mathematics & Theoretical Computer Science, 2006 We investigate class of well-poised basic hypergeometric series $\tilde{J}_{k,i}(a;x;q)$, interpreting these series as generating functions for overpartitions defined by multiplicity conditions.
Sylvie Corteel +2 more
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Axioms, 2013 Recently, the authors have established a large class of modular relations involving the Rogers-Ramanujan type functions J(q) and K(q) of order ten. In this paper, we establish further modular relations connecting these two functions with Rogers-Ramanujan
Nasser Abdo Saeed Bulkhali +1 more
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Colored Partitions and the Fibonacci Sequence
Trends in Computational and Applied Mathematics, 2006 We present interesting combinatorial interpretations for the Fibonacci numbers in terms of colored partitions obtained by using finite versions of two identities of the Rogers-Ramanujan type. New formula for the Fibonacci numbers is also given.
J.P.O. Santos, M. Ivkovic
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Modular relations for the Rogers-Ramanujan-Slater type functions of order fifteen and its applications to partitions [PDF]
Romanian Journal of Mathematics and Computer Science, 2013 In a manuscript of Ramanujan, published with his Lost Notebook [20] there are forty identities involving the Rogers-Ramanujan functions. In this paper, we establish several modular relations involving the Rogers-Ramanujan functions and the Rogers ...
Chandrashekar Adiga +2 more
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