An Improper Integral, the Beta Function, the Wallis Ratio, and the Catalan Numbers

DOI10.15393/j3.art.2018.4370zbMath1440.11023OpenAlexW2887666079WikidataQ129427222 ScholiaQ129427222MaRDI QIDQ5204619

Feng Qi

Publication date: 4 December 2019

Published in: Issues of Analysis (Search for Journal in Brave)

Full work available at URL: http://mathnet.ru/eng/pa229

zbMATH Keywords

beta functionCatalan numberintegral representationWallis ratioclosed expressionimproper integralunified expression

Mathematics Subject Classification ID

Binomial coefficients; factorials; (q)-identities (11B65) Gamma, beta and polygamma functions (33B15) Other combinatorial number theory (11B75) Integrals of Riemann, Stieltjes and Lebesgue type (26A42) Special sequences and polynomials (11B83) Denjoy and Perron integrals, other special integrals (26A39)

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Uses Software

• DLMF

Cites Work

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• Some best approximation formulas and inequalities for the Wallis ratio
• Schur-convexity of the Catalan-Qi function related to the Catalan numbers
• Bounds for the ratio of two gamma functions
• Parametric integrals, the Catalan numbers, and the beta function
• Parametric improper integrals, Wallis formula and Catalan numbers
• On Wallis' formula

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