期刊全稱 | A Generalization of Bohr-Mollerup‘s Theorem for Higher Order Convex Functions | 影響因子2023 | Jean-Luc Marichal,Na?m Zena?di | 視頻video | http://file.papertrans.cn/141/140854/140854.mp4 | 發(fā)行地址 | This book is open access, which means that you have free and unlimited access.Gives a far-reaching generalization of the famous Bohr-Mollerup theorem from 1922.Provides a unified setting for the inves | 學(xué)科分類 | Developments in Mathematics | 圖書封面 |  | 影響因子 | In 1922, Harald Bohr and Johannes Mollerup established a remarkable characterization of the Euler gamma function using its log-convexity property. A decade later, Emil Artin investigated this result and used it to derive the basic properties of the gamma function using elementary methods of the calculus. Bohr-Mollerup‘s theorem was then adopted by Nicolas Bourbaki as the starting point for his exposition of the gamma function..This open access book develops a far-reaching generalization of Bohr-Mollerup‘s theorem to higher order convex functions, along lines initiated by Wolfgang Krull, Roger Webster, and some others but going considerably further than past work. In particular, this generalization shows using elementary techniques that a very rich spectrum of functions satisfy analogues of several classical properties of the gamma function, including Bohr-Mollerup‘s theorem itself, Euler‘s reflection formula, Gauss‘ multiplication theorem, Stirling‘s formula, and Weierstrass‘ canonical factorization..The scope of the theory developed in this work is illustrated through various examples, ranging from the gamma function itself and its variants and generalizations (q-gamma, polygamma, | Pindex | Book‘‘‘‘‘‘‘‘ 2022 |
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