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A Generalization of Bohr-Mollerup's Theorem for Higher Order Convex Functions

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datacite.subject.fos oecd::Natural sciences::Mathematics
dc.contributor.author Jean-Luc Marichal, Naïm Zenaïdi
dc.date.accessioned 2023-06-26T09:31:13Z
dc.date.available 2023-06-26T09:31:13Z
dc.date.issued 2022
dc.description DOI: https://doi.org/10.1007/978-3-030-95088-0 License: CC BY; Publisher: Springer
dc.description.abstract 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, multiple gamma functions) to important special functions such as the Hurwitz zeta function and the generalized Stieltjes constants.This volume is also an opportunity to honor the 100th anniversary of Bohr-Mollerup's theorem and to spark the interest of a large number of researchers in this beautiful theory.
dc.identifier.doi https://doi.org/10.1007/978-3-030-95088-0
dc.identifier.isbn 9783030950880
dc.identifier.uri http://repository.vlu.edu.vn:443/handle/123456789/5904
dc.language.iso en
dc.subject Difference Equation
dc.subject Higher Order Convexity
dc.subject Bohr-Mollerup's Theorem
dc.subject Principal Indefinite Sums
dc.subject Gauss' Limit
dc.subject Euler Product Form
dc.subject Raabe's Formula
dc.subject Binet's Function
dc.subject Stirling's Formula
dc.subject Euler's Infinite Product
dc.subject Euler's Reflection Formula
dc.subject Weierstrass' Infinite Product
dc.subject Gauss Multiplication Formula
dc.subject Euler's Constant
dc.subject Gamma Function
dc.subject Polygamma Functions
dc.subject Hurwitz Zeta Function
dc.subject Generalized Stieltjes Constants.
dc.title A Generalization of Bohr-Mollerup's Theorem for Higher Order Convex Functions
dc.type Resource Types::text::book
dspace.entity.type Publication
oairecerif.author.affiliation #PLACEHOLDER_PARENT_METADATA_VALUE#
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