Results 81 to 90 of about 505,916 (139)
Elementary proofs of some identities of Ramanujan for the Rogers-Ramanujan functions [PDF]
, 2012 In a handwritten manuscript published with his lost notebook, Ramanujan stated without proofs forty identities for the Rogers-Ramanujan functions. With one exception all of Ramanujan's identities were proved.
Yesilyurt, H. +2 more
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On the infinite Borwein product raised to a positive real power. [PDF]
Ramanujan J, 2023 Schlosser MJ, Zhou NH.
europepmc +1 more source
Weighted cylindric partitions. [PDF]
J Algebr Comb (Dordr), 2022 Bridges W, Uncu AK.
europepmc +1 more source
Asymptotic analogs of the Rogers-Ramanujan identities
Journal of Combinatorial Theory, Series A, 1986 Let p(n,S) be the number of partitions of n with parts belonging to the set S; let q(n,S) be the number of partitions of n with parts distinct and belonging to the set S; let \(q_ d(n)\) be the number of partitions of n with parts differing by at least d. Asymptotic formulas for p(n,S), q(n,S), and \(q_ d(n)\) are derived.
openaire +2 more sources
Affine Lie Algebras, Vertex Operator Algebras and Combinatorial Identities
, 2005 Affine Lie algebra representations have many connections with different areas of mathematics and physics. One such connection in mathematics is with number theory and in particular combinatorial identities.
Cook, William Jeffrey
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Combinatorial Interpretation of Rogers Ramanujan Identities and Their Analogues
, 2012 M.Sc. (Mathematics and Computing)In this thesis, we study about partitions of positive integers. The study of parti- tions of positive integers has fascinated a number of great mathematicians: Euler, Legendre, Ramanujan, Hardy, Rademacher, Sylvester ...
Bansal, Rajni
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Overpartitions, lattice paths and Rogers-Ramanujan identities
, 2006 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 ...
Mallet, Olivier, Corteel, Sylvie
core
Identities for the Rogers-Ramanujan Continued Fraction
We prove some new modular identities for the Rogers\textendash Ramanujan continued fraction. For example, if $R(q)$ denotes the Rogers\textendash Ramanujan continued fraction, then \begin{align*}&R(q)R(q^4)=\dfrac{R(q^5)+R(q^{20})-R(q^5)R(q^{20})}{1+R(q^{5})+R(q^{20})},\\ &\dfrac{1}{R(q^{2})R(q^{3})}+R(q^{2})R(q^{3})= 1+\dfrac{R(q)}{R(q^{6 ...
Baruah, Nayandeep Deka +1 more
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Ramanujan's influence on string theory, black holes and moonshine. [PDF]
Philos Trans A Math Phys Eng Sci, 2020 Harvey JA.
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Some New q-Congruences for Truncated Basic Hypergeometric Series: Even Powers. [PDF]
Results Math, 2020 Guo VJW, Schlosser MJ.
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