Results 61 to 70 of about 505,916 (139)
Comment on “Some Congruence Properties of a Restricted Bipartition Function cN(n)”
, 2017 International Journal of Analysis, Volume 2017, Issue 1, 2017.
Qing Zou, Ahmed Zayed
wiley +1 more source
A Note on Four‐Variable Reciprocity Theorem
International Journal of Mathematics and Mathematical Sciences, Volume 2009, Issue 1, 2009., 2009 We give new proof of a four‐variable reciprocity theorem using Heine′s transformation, Watson′s transformation, and Ramanujan′s 1 ψ 1‐summation formula. We also obtain a generalization of Jacobi′s triple product identity.
Chandrashekar Adiga +2 more
wiley +1 more source
Rogers-Ramanujan type identities for alternating knots [PDF]
, 2016 We highlight the role of q-series techniques in proving identities arising from knot theory. In particular, we prove Rogers–Ramanujan type identities for alternating knots as conjectured by Garoufalidis, Lê and ...
Osburn, Robert, Keilthy, Adam
core +1 more source
Transactions of the London Mathematical Society, Volume 12, Issue 1, December 2025.Abstract The representation of an analytic function as a series involving q$q$‐polynomials is a fundamental problem in classical analysis and approximation theory [Ramanujan J. 19 (2009), no. 3, 281–303]. In this paper, our investigation is focusing on q$q$‐analog complex Hermite polynomials, which were motivated by Ismail and Zhang [Adv. Appl.
Jian Cao
wiley +1 more source
Partitions in real quadratic fields
Mathematische Nachrichten, Volume 298, Issue 2, Page 548-566, February 2025.Abstract We study partitions of totally positive integers in real quadratic fields. We develop an algorithm for computing the number of partitions, prove a result about the parity of the partition function, and characterize the quadratic fields such that there exists an element with exactly 1–5, 7, and 11 partitions.
David Stern, Mikuláš Zindulka
wiley +1 more source
A-D-E POLYNOMIAL AND ROGERS-RAMANUJAN IDENTITIES [PDF]
International Journal of Modern Physics A, 1996 We conjecture polynomial identities which imply Rogers-Ramanujan type identities for branching functions associated with the cosets [Formula: see text], with [Formula: see text], Dn–1 (ℓ≥2), E6,7,8 (ℓ=2). In support of our conjectures we establish the correct behavior under level-rank duality for [Formula: see text] and show that the A–D–E Rogers ...
Warnaar, S. Ole, Pearce, Paul A.
openaire +2 more sources
Partition theorems related to the Rogers-Ramanujan identities [PDF]
, 1967 In this paper a partition theorem is proved which contains the Rogers-Ramanujan identities and Euler's partition theorem as special cases.
Andrews, George E.
core +1 more source
An easy proof of the Rogers-Ramanujan identities [PDF]
, 1983 A proof of the Rogers-Ramanujan identities is presented which is brief, elementary, and well motivated; the “easy” proof of whose existence Hardy and Wright had despaired.
Bressoud, D.M.
core +1 more source
Engel Expansions and the Rogers–Ramanujan Identities
Journal of Number Theory, 2000 The authors introduce a generalization of the notion of Engel series and use it to give new proofs of identities first proven by Euler, Jacobi and Rogers and Ramanujan. The Engel series is an algorithm for representing real numbers and is of the form \(t=\sum^\infty_{n=1} {1\over a_1a_2\cdots a_n}\), where \(a_1,a_2, \dots\) is a non-decreasing ...
Andrews, George E. +2 more
openaire +1 more source
The $A_2$ Rogers-Ramanujan identities revisited
, 2019 published in Annals of Combinatorics for the 80th birthday of George ...
Corteel, Sylvie, Welsh, Trevor
openaire +3 more sources