Mathematics, Vol. 11, Pages 1870: A Brief Survey and an Analytic Generalization of the Catalan Numbers and Their Integral Representations

Mathematics, Vol. 11, Pages 1870: A Brief Survey and an Analytic Generalization of the Catalan Numbers and Their Integral Representations

Mathematics doi: 10.3390/math11081870

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

In the paper, the authors briefly survey several generalizations of the Catalan numbers in combinatorial number theory, analytically generalize the Catalan numbers, 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 for further study.