An Integral Representation, Complete Monotonicity, and Inequalities of the Catalan Numbers

Feng Qi, Xiao-Ting Shi, Fang-Fang Liu


In the paper, by virtue of the Cauchy integral formula in the theory of complex functions, the authors establish an integral representation for the generating function of the Catalan numbers in combinatorics. From this, the authors derive an alternative integral representation, complete monotonicity, determinantal and product inequalities for the Catalan numbers.

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