Results 1 to 10 of about 128 (110)
On identities of the Rogers-Ramanujan type [PDF]
Ramanujan Journal, 2006 A generalized Bailey pair, which contains several special cases considered by Bailey (\emph{Proc. London Math. Soc. (2)}, 50 (1949), 421--435), is derived and used to find a number of new Rogers-Ramanujan type identities. Consideration of associated $q$-difference equations points to a connection with a mild extension of Gordon's combinatorial ...
Andrew Sills
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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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New Enumerations for l-Regular Bipartitions Under Modulo 2 and 3
Journal of MathematicsFor any positive integer l, Bln represents the number of l-regular bipartitions. By employing q-identities, modular equations, and Rogers–Ramanujan continued fraction identities, we establish new congruences under modulo 2 and 3.
null Maheshagouda, B. R. Srivatsa Kumar
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Variants of the Rogers–Ramanujan Identities
Advances in Applied Mathematics, 1999 In 1894, L. J. Rogers published an analysis of what today are called the \(q\)-Hermite and \(q\)-ultraspherical polynomials. Of the many identities he generated in this paper, the best known are the Rogers-Ramanujan identities. The authors of this paper go back to Rogers, simplify his proof by explicitly using the orthogonality of these polynomials ...
Dennis Stanton
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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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Identities of the Rogers–Ramanujan–Bailey type
Journal of Mathematical Analysis and Applications, 2005 23 ...
Andrew Sills
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Partial-Sum Analogues of the Rogers–Ramanujan Identities
Journal of Combinatorial Theory - Series A, 2002 A new type of polynomial analogue of the Rogers-Ramanujan identities is proven. Here the product-side of the Rogers-Ramanujan identities is replaced by a partial theta sum and the sum-side by a weighted sum over Schur polynomials.
S Ole Warnaar
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Overpartitions, lattice paths, and Rogers–Ramanujan identities
Journal of Combinatorial Theory - Series A, 2007 We extend partition-theoretic work of Andrews, Bressoud, and Burge to overpartitions, defining the notions of successive ranks, generalized Durfee squares, and generalized lattice paths, and then relating these to overpartitions defined by multiplicity conditions on the parts.
Sylvie Corteel
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A graphic illustration of Rogers-Ramanujan Identities
Applied Mathematics Letters, 1996 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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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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