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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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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A short derivation of an elegant sum involving central binomial coefficients due to László via a hypergeometric series approach [PDF]
Contributions to Mathematics, 2022 The aim of this short note is to establish an elegant sum involving central binomial coefficients, due to L´aszl´o [ Amer. Math. Monthly 108 (2001) 851–855], via a hypergeometric series approach.
Dongkyu Lim, Arjun K. Rathie
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Several identities containing central binomial coefficients and derived from series expansions of powers of the arcsine function [PDF]
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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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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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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Series associated with harmonic numbers, Fibonacci numbers and central binomial coefficients $binom{2n}{n}$ [PDF]
Notes on Number Theory and Discrete MathematicsWe find various series that involve the central binomial coefficients $binom{2n}{n}$, harmonic numbers and Fibonacci numbers. Contrary to the traditional hypergeometric function _pF_q approach, our method utilizes a straightforward transformation to ...
Segun Olofin Akerele +1 more
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Harmonic Series of Convergence Ratio “1/4" with Cubic Central Binomial Coefficients
AxiomsWe examine a useful hypergeometric transformation formula by means of the coefficient extraction method. A large class of “binomial/harmonic series” (of convergence ratio “1/4”) containing the cubic central binomial coefficients and harmonic numbers is ...
Chunli Li, Wenchang Chu
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Odd Euler Sums and Harmonic Series with Cubic Central Binomial Coefficients in Denominators
AxiomsBy means of the coefficient extraction method, we examine a transformation of a classical hypergeometric series. Three classes of infinite series (of convergence rate “1/4”) with harmonic numbers in numerators and cubic central binomial coefficients in ...
Chunli Li, Wenchang Chu
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Fifteen series on harmonic numbers and quintic central binomial coefficients [PDF]
Discrete Mathematics LettersChunli Li, Wenchang Chu
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