A Generalization of Bohr-Mollerup's Theorem for Higher Order Convex Functions
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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| Príomhchruthaitheoirí: | , |
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| Údar corparáideach: | |
| Formáid: | Leictreonach Ríomhleabhar |
| Teanga: | Béarla |
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Cham :
Springer International Publishing : Imprint: Springer,
2022.
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| Eagrán: | 1st ed. 2022. |
| Sraith: | Developments in Mathematics,
70 |
| Ábhair: | |
| Rochtain ar líne: | Link to Metadata |
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Clár na nÁbhar:
- 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.