Geodesic
An improper integral, the beta function, the Wallis ratio, and the Catalan numbers
Problemy analiza, Tome 7 (2018) no. 1, pp. 104-115

Voir la notice de l'article provenant de la source Math-Net.Ru

In the paper we present closed and unified expressions for a sequence of improper integrals in terms of the beta function and the Wallis ratio. Hereafter, we derive integral representations for the Catalan numbers originating from combinatorics.
Keywords: improper integral; closed expression; unified expression; beta function; Wallis ratio; integral representation; Catalan number. 
@article{PA_2018_7_1_a6,
     author = {Qi Feng},
     title = {An improper integral, the beta function, the {Wallis} ratio, and the {Catalan} numbers},
     journal = {Problemy analiza},
     pages = {104--115},
     publisher = {mathdoc},
     volume = {7},
     number = {1},
     year = {2018},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/PA_2018_7_1_a6/}
}
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Qi Feng. An improper integral, the beta function, the Wallis ratio, and the Catalan numbers. Problemy analiza, Tome 7 (2018) no. 1, pp. 104-115. http://geodesic.mathdoc.fr/item/PA_2018_7_1_a6/