Asymptotic expansions of integral means and applications to the ratio of gamma functions

2013/12/05 by Neven Elezović, Elezović, Neven, Lenka Vukšić +1 · 1 citation
Mathematics · #33B15 #41A60 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #math.CA #msc:33B15 #msc:41A60

paper · pdf · doi:10.48550/arxiv.1312.1500

arxiv created 2013/12/05 · arxiv updated 2013/12/06

Abstract

Integral means are important class of bivariate means. In this paper we prove the very general algorithm for calculation of coefficients in asymptotic expansion of integral mean. It is based on explicit solving the equation of the form B(A(x))=C(x), where B and C have known asymptotic expansions. The results are illustrated by calculation of some important integral means connected with gamma and digamma functions.

Cited by

• Expansion of a bivariate symmetric mean in the neighborhood of the first bisector

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