A Generalization of Bohr-Mollerup's Theorem for Higher Order Convex Functions
Springer International Publishing (Verlag)
978-3-030-95087-3 (ISBN)
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.
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.
Preface.- List of main symbols.- Table of contents.- Chapter 1. Introduction.- Chapter 2. Preliminaries.- Chapter 3. Uniqueness and existence results.- Chapter 4. Interpretations of the asymptotic conditions.- Chapter 5. Multiple log-gamma type functions.- Chapter 6. Asymptotic analysis.- Chapter 7. Derivatives of multiple log-gamma type functions.- Chapter 8. Further results.- Chapter 9. Summary of the main results.- Chapter 10. Applications to some standard special functions.- Chapter 11. Definining new log-gamma type functions.- Chapter 12. Further examples.- Chapter 13. Conclusion.- A. Higher order convexity properties.- B. On Krull-Webster's asymptotic condition.- C. On a question raised by Webster.- D. Asymptotic behaviors and bracketing.- E. Generalized Webster's inequality.- F. On the differentiability of sigma_g.- Bibliography.- Analogues of properties of the gamma function.- Index.
| Erscheinungsdatum | 08.07.2022 |
|---|---|
| Reihe/Serie | Developments in Mathematics |
| Zusatzinfo | XVIII, 323 p. |
| Verlagsort | Cham |
| Sprache | englisch |
| Maße | 155 x 235 mm |
| Gewicht | 673 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Analysis |
| Schlagworte | Analysis • Binet's function • Bohr-Mollerup's theorem • Convexity • difference equation • Difference Equations • Euler product form • Euler's constant • Euler's infinite product • Euler's Reflection Formula • gamma function • Gauss' limit • Gauss multiplication formula • Generalized Stieltjes constants • higher order convexity • Hurwitz zeta function • Mathematics • open access • Polygamma functions • Principal indefinite sums • Raabe's formula • Stirling's formula • Weierstrass' infinite product |
| ISBN-10 | 3-030-95087-5 / 3030950875 |
| ISBN-13 | 978-3-030-95087-3 / 9783030950873 |
| Zustand | Neuware |
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