Some properties of the Catalan-Qi function related to the Catalan numbers.

ABSTRACT: In the paper, the authors find some properties of the Catalan numbers, the Catalan function, and the Catalan-Qi function which is a generalization of the Catalan numbers. Concretely speaking, the authors present a new expression, asymptotic expansions, integral representations, logarithmic convexity, complete monotonicity, minimality, logarithmically complete monotonicity, a generating function, and inequalities of the Catalan numbers, the Catalan function, and the Catalan-Qi function. As by-products, an exponential expansion and a double inequality for the ratio of two gamma functions are derived.

SUBMITTER: Qi F 

PROVIDER: S-EPMC4951397 | biostudies-other | 2016

REPOSITORIES: biostudies-other