An integral representation of Catalan numbers using Malmstén's formula

2024/08/09 by Pain, Jean-Christophe
#Combinatorics (math.CO) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2408.05130

Abstract

In this article, we propose an integral expression of the Catalan numbers, based on Malmstén's definite-integral representation of ln[Γ(x)], Γ being the usual Gamma function. The obtained expression is likely to yield new summations involving Catalan numbers or central binomial coefficients.

Related

• An integral representation of Catalan numbers using the Féaux formula
• Integral representations of Catalan numbers using Touchard-like identities
• Two New Identities Involving the Catalan Numbers: A classical approach
• Catalan and Motzkin Integral Representations
• Some identities and formulas involving generalized Catalan numbers