Results 41 to 50 of about 505,916 (139)

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, Chayanika Boruah, Ahmed Zayed   +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., Chaudhary Sangeeta, Minz Sonajharia   +2 more
doaj  

A Note on the Rogers‐Ramanujan identities

Mathematische Nachrichten, 1958
Verf. gibt neue Beweise für die Identitäten \[ \sum_{m=0}^\infty \frac{q^{m^2}}{(q)_m} = \prod_{m=0}^\infty (1-q^{5m+1})^{-1} (1-q^{5m+4})^{-1}, \] \[ \sum_{m=0}^\infty \frac{q^{m^2+m}}{(q)_m} = \prod_{m=0}^\infty (1-q^{5m+2})^{-1} (1-q^{5m+3})^{-1}, \] wo \((q)_m = (1-q)(1-q^2)\cdots (1-q^m)\), \((q)_0=1\).
openaire   +3 more sources

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, A. Vanitha, M. S. Surekha, Ahmed Laghribi   +3 more
wiley   +1 more source

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, Maslina Darus, Jacek Dziok   +2 more
wiley   +1 more source

On a generalized basic series and Rogers-Ramanujan type identities [PDF]

, 2023
In this paper, we give the generalization of MacMahon\u27s type combinatorial identities. A generalized $q$-series is interpreted as the generating function of two different combinatorial objects, viz., restricted $n$-color partitions and weighted ...
Ranganatha, D., Goyal, Megha, Sonik, Pooja   +2 more
core   +2 more sources

A Determinant Identity that Implies Rogers-Ramanujan [PDF]

The Electronic Journal of Combinatorics, 2005
We give a combinatorial proof of a general determinant identity for associated polynomials. This determinant identity gives rise to new polynomial generalizations of known Rogers-Ramanujan type identities. Several examples of new Rogers-Ramanujan type identities are given.
openaire   +3 more sources

New Proofs of Some q‐Summation and q‐Transformation Formulas

The Scientific World Journal, Volume 2014, Issue 1, 2014., 2014
We obtain an expectation formula and give the probabilistic proofs of some summation and transformation formulas of q‐series based on our expectation formula. Although these formulas in themselves are not the probability results, the proofs given are based on probabilistic concepts.
Xian-Fang Liu, Ya-Qing Bi, Qiu-Ming Luo, Kishin Sadarangani   +3 more
wiley   +1 more source

Revisiting a Classic Identity That Implies the Rogers–Ramanujan Identities III

Mathematics
This is the third installment in a series of papers on a one-parameter extension of the Rogers–Ramanujan identities (this extension was discovered independently by Rogers and Ramanujan). In this paper, we report a new proof of this identity.
Hei-Chi Chan
doaj   +1 more source

New Partition Theoretic Interpretations of Rogers‐Ramanujan Identities

International Journal of Combinatorics, Volume 2012, Issue 1, 2012., 2012
The generating function for a restricted partition function is derived. This in conjunction with two identities of Rogers provides new partition theoretic interpretations of Rogers‐Ramanujan identities.
A. K. Agarwal, M. Goyal, Toufik Mansour
wiley   +1 more source