An analytic generalization of the Catalan numbers and its integral representation

Feng Qi, Wen-Hui Li, Jian Cao, Da-Wei Niu, Jiao-Lian Zhao

Published 2020-05-26Version 1

In the paper, the authors analytically generalize the Catalan numbers in combinatorial number theory, establish an integral representation of the analytic generalization of the Catalan numbers by virtue of Cauchy's integral formula in the theory of complex functions, and point out potential directions to further study.