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Bilateral identities of the Rogers--Ramanujan type [PDF]
, 2023 We derive by analytic means a number of bilateral identities of the Rogers--Ramanujan type. Our results include bilateral extensions of the Rogers--Ramanujan and the G\"ollnitz-Gordon identities, and of related identities by Ramanujan, Jackson, and ...
Schlosser, Michael J.
core
The Rogers-Ramanujan Identities [PDF]
, 2015 In 1894, Rogers found the two identities for the first time. In 1913, Ramanujan found the two identities later and then the two identities are known as The Rogers-Ramanujan Identities.
Hossain, Fazlee, Das, Sabuj
core +2 more sources
On a Combinatorial Result Related to the Rogers-Ramanujan Identities
Trends in Computational and Applied Mathematics, 2000 We give a generating function for partitions with different conditions and a combinatorial proof for a bijection between these partitions and another class of partitions.
J.P.O. Santos, P. Mondek
doaj +1 more source
A new proof of some identities of Bressoud
International Journal of Mathematics and Mathematical Sciences, 2002 We provide a new proof of the following two identities due to Bressoud: ∑m=0Nqm2[Nm]=∑m=−∞∞(−1)mqm(5m+1)/2 [ 2NN+2m], ∑m=0Nqm2+m[Nm]=(1/(1−qN+1))∑m=−∞∞(−1)m×qm(5m+3)/2 [ 2N+2N+2m+2], which can be considered as finite versions of the Rogers ...
Robin Chapman
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A Generalized Inverse Binomial Summation Theorem and Some Hypergeometric Transformation Formulas
International Journal of Combinatorics, Volume 2016, Issue 1, 2016., 2016 A generalized binomial theorem is developed in terms of Bell polynomials and by applying this identity some sums involving inverse binomial coefficient are calculated. A technique is derived for calculating a class of hypergeometric transformation formulas and also some curious q series identities.
S. M. Ripon, Toufik Mansour
wiley +1 more source
Some Congruence Properties of a Restricted Bipartition Function cN(n)
International Journal of Analysis, Volume 2016, Issue 1, 2016., 2016 Let cN(n) denote the number of bipartitions (λ, μ) of a positive integer n subject to the restriction that each part of μ is divisible by N. In this paper, we prove some congruence properties of the function cN(n) for N = 7, 11, and 5l, for any integer l≥1, by employing Ramanujan’s theta‐function identities.
Nipen Saikia +2 more
wiley +1 more source
On relationships between q-product identities and combinatorial partition identities [PDF]
Mathematica Moravica, 2020 Andrews et al. [2] discussed about the combinatorial partition identities. We aim to present some relationships between q-product identities and combinatorial partition identities, by using and combining known formulas.
Chaudhary M.P. +2 more
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Continued Fractions of Order Six and New Eisenstein Series Identities
Journal of Numbers, Volume 2014, Issue 1, 2014., 2014 We prove two identities for Ramanujan’s cubic continued fraction and a continued fraction of Ramanujan, which are analogues of Ramanujan’s identities for the Rogers‐Ramanujan continued fraction. We further derive Eisenstein series identities associated with Ramanujan’s cubic continued fraction and Ramanujan’s continued fraction of order six.
Chandrashekar Adiga +3 more
wiley +1 more source
Variants of the Rogers–Ramanujan Identities [PDF]
, 1999 We evaluate several integrals involving generating functions of continuous q-Hermite polynomials in two different ways. The resulting identities give new proofs and generalizations of the Rogers–Ramanujan identities. Two quintic transformations are given,
Stanton, Dennis +2 more
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A New Class of Meromorphic Functions Involving the Polylogarithm Function
Journal of Complex Analysis, Volume 2014, Issue 1, 2014., 2014 We introduce a new operator Dcf(z) associated with polylogarithm function. By making use of the new operator, we define a certain new class of meromorphic functions and discussed some important properties of it.
Khadeejah Rasheed Alhindi +2 more
wiley +1 more source