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A Note on Generalization of Combinatorial Identities Due to Gould and Touchard
Axioms, 2023 Using a hypergeometric series approach, a general combinatorial identity is found in this note, and among its special cases are well-known and classical combinatorial identities due to Gould and Touchard.
Arjun K Rathie, Dongkyu Lim
exaly +3 more sources
Mathematics, 2020 The authors establish a set of six new theta-function identities involving multivariable R-functions which are based upon a number of q-product identities and Jacobi’s celebrated triple-product identity.
H M Srivastava +2 more
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A class of combinatorial identities
Discrete Mathematics, 2006 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Yingpu Deng
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Some combinatorial identities involving noncommuting variables [PDF]
Discrete Mathematics & Theoretical Computer Science, 2015 We derive combinatorial identities for variables satisfying specific sets of commutation relations. The identities thus obtained extend corresponding ones for $q$-commuting variables $x$ and $y$ satisfying $yx=qxy$.
Michael Schlosser, Meesue Yoo
doaj +1 more source
Results in Nonlinear Analysis, 2021 In the paper, with the aid of the series expansions of the square or cubic of the arcsine function, the authors establish several possibly new combinatorial identities containing the ratio of two central binomial coefficients which are related to the ...
Feng Qi, Chao-Ping Chen , Dongkyu Lim
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Some extensions for the several combinatorial identities
Advances in Difference Equations, 2021 In this paper, we give some extensions for Mortenson’s identities in series with the Bell polynomial using the partial fraction decomposition. As applications, we obtain some combinatorial identities involving the harmonic numbers.
Gao-Wen Xi, Qiu-Ming Luo
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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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New Expressions for Sums of Products of the Catalan Numbers
Axioms, 2021 In this paper, we perform a further investigation for the Catalan numbers. By making use of the method of derivatives and some properties of the Bell polynomials, we establish two new expressions for sums of products of arbitrary number of the Catalan ...
Conghui Xie, Yuan He
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Special Numbers and Polynomials Including Their Generating Functions in Umbral Analysis Methods
Axioms, 2018 In this paper, by applying umbral calculus methods to generating functions for the combinatorial numbers and the Apostol type polynomials and numbers of order k, we derive some identities and relations including the combinatorial numbers, the Apostol ...
Yilmaz Simsek
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A Note on the Difference of Powers and Falling Powers
International Journal of Mathematics and Mathematical Sciences, 2021 Combinatorial sums and binomial identities have appeared in many branches of mathematics, physics, and engineering. They can be established by many techniques, from generating functions to special series.
Taoufik Sabar
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