A generalization of Bohr-Mollerup's theorem for higher order convex functions: a tutorial

DOI10.1007/s00010-023-00968-9arXiv2207.12694OpenAlexW4381856123WikidataQ122956752 ScholiaQ122956752MaRDI QIDQ6130585

Jean-Luc Marichal, Naïm Zenaïdi

Publication date: 3 April 2024

Published in: Aequationes Mathematicae (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2207.12694

zbMATH Keywords

gamma and polygamma functionsdifference equationStirling's formulaEuler's constantRaabe's formulahigher order convexityGauss' multiplication formulaBinet's functionBohr-Mollerup's theoremEuler product formGauss' limitprincipal indefinite sum

Mathematics Subject Classification ID

Functional equations for real functions (39B22) Gamma, beta and polygamma functions (33B15) Convexity of real functions in one variable, generalizations (26A51) Incomplete beta and gamma functions (error functions, probability integral, Fresnel integrals) (33B20) Linear difference equations (39A06)

Cites Work

• Expansions of generalized Euler's constants into the series of polynomials in \(\pi^{- 2}\) and into the formal enveloping series with rational coefficients only
• Polygamma functions of negative order
• Log-convex solutions to the functional equation \(f(x+1)=g(x)f(x):\Gamma\)-type functions
• The Cauchy numbers
• Special solutions of certain difference equations
• A generalization of Bohr-Mollerup's theorem for higher order convex function
• An Elementary View of Euler's Summation Formula
• The Gamma Function: An Eclectic Tour
• Bemerkungen zur Differenzengleichung g (x + 1) − g(x) = φ (x). Helmut Hasse zum 50. Geburtstag
• Bemerkungen zur Differenzengleichung g(x + 1) – g(x) = φ (x). II
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