Parametric integrals, the Catalan numbers, and the beta function

DOI10.4171/EM/332zbMath1440.11022OpenAlexW2738678714MaRDI QIDQ1681064

Feng Qi

Publication date: 17 November 2017

Published in: Elemente der Mathematik (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.4171/em/332

zbMATH Keywords

beta functionCatalan numbersWallis ratio

Mathematics Subject Classification ID

Binomial coefficients; factorials; (q)-identities (11B65) Gamma, beta and polygamma functions (33B15)

Related Items (14)

Some inequalities involving the extended gamma function and the Kummer confluent hypergeometric \(k\)-function ⋮ Several explicit and recursive formulas for generalized Motzkin numbers ⋮ The inverse of a triangular matrix and several identities of the Catalan numbers ⋮ Integral representations of the Catalan numbers and their applications ⋮ Explicit formulas and recurrence relations for generalized Catalan numbers ⋮ Unnamed Item ⋮ Unnamed Item ⋮ An Improper Integral, the Beta Function, the Wallis Ratio, and the Catalan Numbers ⋮ Several formulas and identities related to Catalan-Qi and \(q\)-Catalan-Qi numbers ⋮ Generalized fractional integral inequalities of Hermite-Hadamard type for \((\alpha,m)\)-convex functions ⋮ Several series identities involving the Catalan numbers ⋮ Some new identities and inequalities for Bernoulli polynomials and numbers of higher order related to the Stirling and Catalan numbers ⋮ Some properties of the Fuss-Catalan numbers ⋮ An integral representation, complete monotonicity, and inequalities of the Catalan numbers

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