Integral Representations of Catalan Numbers and Sums Involving Central Binomial Coefficients

In the paper, the authors collect several integral representations of the Catalan numbers and central binomial coefficients, supply alternative proofs of two integral representations of the Catalan numbers, and apply these integral representations to alternatively prove several combinatorial identities for finite and infinite sums in which central binomial coefficients are involved.

Related Organizations

Department of Mathematics Education
Indonesia
Andong National University
Korea (Republic of)
Henan Polytechnic University
China (People's Republic of)

Keywords

Binomial coefficients; factorials; \(q\)-identities, integral representations, Catalan numbers, central binomial coefficients, Factorials, binomial coefficients, combinatorial functions, Gamma, beta and polygamma functions

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