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Bilateral Bailey pairs and Rogers-Ramanujan type identities
Rogers-Ramanujan type identities occur in various branches of mathematics and physics. As a classic and powerful tool to deal with Rogers-Ramanujan type identities, the theory of Bailey\u27s lemma has been extensively studied and generalized.
Liu, Xiangxin, Sun, Lisa Hui
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A Determinant Identity that Implies Rogers-Ramanujan
, 2008 We give a combinatorial proof of a general determinant identity for associated polynomials. This determinant identity, Theorem 2.2, gives rise to new polynomial generalizations of known Rogers-Ramanujan type identities.
Kristina C. Garrett
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On the Rogers-Ramanujan identities and partition congruences
A research report submitted in partial fulfilment of the requirements for the degree Master of Science to the Faculty of Science, School of Mathematics, University of the Witwatersrand, Johannesburg, 2023In this dissertation, we study the Rogers ...
Seleka, Phodiso
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An Invitation to the Rogers-Ramanujan Identities
Notices of the American Mathematical Society, 2020 openaire +1 more source
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Generalizations of Rogers–Ramanujan type identities
Ramanujan JournalzbMATH Open Web Interface contents unavailable due to conflicting licenses.
S -P Cui, Nancy Gu, Cui Su-Ping
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An Invitation to the ROGERS-RAMANUJAN IDENTITIES
, 2017 Book Summary: The Rogers--Ramanujan identities are a pair of infinite series—infinite product identities that were first discovered in 1894. Over the past several decades these identities, and identities of similar type, have found applications in number
Sills, Andrew V. +2 more
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The Rogers–Ramanujan Identities and the Rogers–Ramanujan Continued Fraction
2017The Rogers–Ramanujan continued fraction is introduced, and two proofs of the Rogers–Ramanujan identifies are given.
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2002
The following two “sum-product” identities (1.1) and (1.2) where $${\left( {a;q} \right)_n} = \prod\limits_{i = 0}^\infty {\frac{{1 - a{q^i}}}{{1 - a{q^{n + 1}}}}} {\text{ }}$$ are known as Rogers-Ramanujan identities. (Note that if n is a positive integer, then (a;q) n = Π i = 0 n − 1 (1 − aq i ); (a;q)0 = 1.) They were ...
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The following two “sum-product” identities (1.1) and (1.2) where $${\left( {a;q} \right)_n} = \prod\limits_{i = 0}^\infty {\frac{{1 - a{q^i}}}{{1 - a{q^{n + 1}}}}} {\text{ }}$$ are known as Rogers-Ramanujan identities. (Note that if n is a positive integer, then (a;q) n = Π i = 0 n − 1 (1 − aq i ); (a;q)0 = 1.) They were ...
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On the Andrews–Schur proof of the Rogers–Ramanujan identities
The Ramanujan Journal, 2010zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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