New asymptotic expansions and Padé approximants related to the triple gamma function

Abstract

In this work, our main focus is to establish asymptotic expansions for the triple gamma function in terms of the triple Bernoulli polynomials. As application, an asymptotic expansion for hyperfactorial function is also obtained. Furthermore, using these asymptotic expansions, Padé approximants related to the triple gamma function are derived as a consequence. The results obtained are new, and their importance is demonstrated by deducing several interesting remarks and corollaries.