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

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

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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 calc...

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Bibliographic Details
Main Authors: Marichal, Jean-Luc (Author), Zenaïdi, Naïm (Author)
Corporate Author: SpringerLink (Online service)
Format: Electronic eBook
Language:English
Published: Cham : Springer International Publishing : Imprint: Springer, 2022.
Edition:1st ed. 2022.
Series:Developments in Mathematics, 70
Subjects:
Special functions.
Difference equations.
Functional equations.
Special Functions.
Difference and Functional Equations.
Online Access:Link to Metadata
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Table of Contents:
  • 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.

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