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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

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

Qi Feng F   Mahmoud Mansour M   Shi Xiao-Ting XT   Liu Fang-Fang FF  

SpringerPlus 20160719 1


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-pro  ...[more]

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