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Synopsis
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.Les informations fournies dans la section « Synopsis » peuvent faire référence à une autre édition de ce titre.
À propos de l?auteur
Jean-Luc Marichal is an Associate Professor of Mathematics at the University of Luxembourg. He completed his PhD in Mathematics in 1998 at the University of Liège (Belgium) and has published about 100 journal papers on aggregation function theory, functional equations, non-additive measures and integrals, conjoint measurement theory, cooperative game theory, and system reliability theory.
Naïm Zenaïdi is a Senior Teaching and Outreach Assistant in the Department of Mathematics at the University of Liège (Belgium). He completed his PhD in Mathematics in 2013 at the University of Brussels (ULB, Belgium) in the field of differential geometry.Les informations fournies dans la section « A propos du livre » peuvent faire référence à une autre édition de ce titre.
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A Generalization of Bohr-Mollerup's Theorem for Higher Order Convex Functions (Developments in Mathematics, 70)
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Generalization of Bohr-mollerup's Theorem for Higher Order Convex Functions
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Generalization of Bohr-mollerup's Theorem for Higher Order Convex Functions
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ISBN 13 : 9783030950873
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Generalization of Bohr-mollerup's Theorem for Higher Order Convex Functions
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Springer, 2022
ISBN 10 : 3030950875
ISBN 13 : 9783030950873
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Couverture rigide
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A Generalization of Bohr Mollerup s Theorem for Higher Order Convex Functions (eng)
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A Generalization of Bohr-Mollerup\ s Theorem for Higher Order Convex Functions
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Gebunden. Etat : New. Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. This book is open access, which means that you have free and unlimited accessGives a far-reaching generalization of the famous Bohr-Mollerup theorem from 1922Provides a unified setting for the investigation of special functionsShows . N° de réf. du vendeur 540229488
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Generalization of Bohr-mollerup's Theorem for Higher Order Convex Functions
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A Generalization of Bohr-Mollerup's Theorem for Higher Order Convex Functions
Edité par
Springer International Publishing, 2022
ISBN 10 : 3030950875
ISBN 13 : 9783030950873
Neuf
Couverture rigide
Vendeur : AHA-BUCH GmbH, Einbeck, Allemagne
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Buch. Etat : Neu. Druck auf Anfrage Neuware - Printed after ordering - 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. N° de réf. du vendeur 9783030950873
Quantité disponible : 1 disponible(s)
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A Generalization of Bohr-Mollerup's Theorem for Higher Order Convex Functions
Edité par
Springer International Publishing Jul 2022, 2022
ISBN 10 : 3030950875
ISBN 13 : 9783030950873
Neuf
Couverture rigide
Vendeur : BuchWeltWeit Ludwig Meier e.K., Bergisch Gladbach, Allemagne
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Buch. Etat : Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -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. 344 pp. Englisch. N° de réf. du vendeur 9783030950873
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A Generalization of Bohr-Mollerup's Theorem for Higher Order Convex Functions
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Hardcover. Etat : Brand New. 341 pages. 9.25x6.10x0.81 inches. In Stock. This item is printed on demand. N° de réf. du vendeur __3030950875
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