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Some combinatorial identities containing central binomial coefficients or Catalan numbers*
Applied Mathematics in Science and Engineering, 2023 In the article, by virtue of Maclaurin's expansions of the arcsine function and its square and cubic, the authors give a short proof of a sum formula of a Maclaurin's series with coefficients containing reciprocals of the Catalan numbers; establish four ...
Feng Qi, Da-Wei Niu, Dongkyu Lim
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Convolution identities involving the central binomial coefficients and Catalan numbers [PDF]
Transactions on Combinatorics, 2021 We generalize some convolution identities due to Witula and Qi et al. involving the central binomial coefficients and Catalan numbers. Our formula allows us to establish many new identities involving these important quantities, and recovers some ...
Necdet Batır, Hakan Kucuk, Sezer Sorgun
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Dirichlet series and series with Stirling numbers
Cubo, 2023 This paper presents a number of identities for Dirichlet series and series with Stirling numbers of the first kind. As coefficients for the Dirichlet series we use Cauchy numbers of the first and second kinds, hyperharmonic numbers, derangement numbers ...
Khristo Boyadzhiev
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Problems for combinatorial numbers satisfying a class of triangular arrays
Lietuvos Matematikos Rinkinys, 2023 Numbers satisfying a class of triangular arrays, defined by a bivariate first-order linear difference equation with linear coefficients, include a wide range of combinatorial numbers: binomial coefficients, Morgan numbers, Stirling numbers of the first ...
Igoris Belovas
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Sums of Pell/Lucas Polynomials and Fibonacci/Lucas Numbers
Mathematics, 2022 Seven infinite series involving two free variables and central binomial coefficients (in denominators) are explicitly evaluated in closed form. Several identities regarding Pell/Lucas polynomials and Fibonacci/Lucas numbers are presented as consequences.
Dongwei Guo, Wenchang Chu
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Some Families of Apéry-Like Fibonacci and Lucas Series
Mathematics, 2021 In this paper, the authors investigate two special families of series involving the reciprocal central binomial coefficients and Lucas numbers. Connections with several familiar sums representing the integer-valued Riemann zeta function are also pointed ...
Robert Frontczak +2 more
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Applications of Lehmer’s Infinite Series Involving Reciprocals of the Central Binomial Coefficients
Journal of Function Spaces, 2022 The main objective of this paper is to establish several new closed-form evaluations of the generalized hypergeometric function Fq+1qz for q=2,3,4,5. This is achieved by means of separating the generalized hypergeometric function Fq+1qz (q=2,3,4,5) into ...
B. R. Srivatsa Kumar +2 more
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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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Moments of the Negative Multinomial Distribution
Mathematical and Computational Applications, 2023 The negative multinomial distribution appears in many areas of applications such as polarimetric image processing and the analysis of longitudinal count data.
Frédéric Ouimet
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Infinite series containing quotients of central binomial coefficients [PDF]
Notes on Number Theory and Discrete MathematicsBy making use of the Wallis' integral formulae and integration by parts, two classes of infinite series are evaluated, in closed form, in terms of π and Riemann zeta function.
Zhiling Fan
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