A Generalization of Bohr-Mollerup's Theorem for Higher Order Convex Functions (Record no. 37761)
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| fixed length control field | 04443nam a22005535i 4500 |
| 001 - CONTROL NUMBER | |
| control field | 978-3-030-95088-0 |
| 003 - CONTROL NUMBER IDENTIFIER | |
| control field | DE-He213 |
| 005 - DATE AND TIME OF LATEST TRANSACTION | |
| control field | 20240508090327.0 |
| 007 - PHYSICAL DESCRIPTION FIXED FIELD--GENERAL INFORMATION | |
| fixed length control field | cr nn 008mamaa |
| 008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION | |
| fixed length control field | 220706s2022 sz | s |||| 0|eng d |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| International Standard Book Number | 9783030950880 |
| -- | 978-3-030-95088-0 |
| 024 7# - OTHER STANDARD IDENTIFIER | |
| Standard number or code | 10.1007/978-3-030-95088-0 |
| Source of number or code | doi |
| 050 #4 - LIBRARY OF CONGRESS CALL NUMBER | |
| Classification number | QA351 |
| 072 #7 - SUBJECT CATEGORY CODE | |
| Subject category code | PBKF |
| Source | bicssc |
| 072 #7 - SUBJECT CATEGORY CODE | |
| Subject category code | MAT034000 |
| Source | bisacsh |
| 072 #7 - SUBJECT CATEGORY CODE | |
| Subject category code | PBKF |
| Source | thema |
| 082 04 - DEWEY DECIMAL CLASSIFICATION NUMBER | |
| Classification number | 515.5 |
| Edition number | 23 |
| 100 1# - MAIN ENTRY--PERSONAL NAME | |
| Personal name | Marichal, Jean-Luc. |
| Relator term | author. |
| Relationship | aut |
| -- | http://id.loc.gov/vocabulary/relators/aut |
| 245 12 - TITLE STATEMENT | |
| Title | A Generalization of Bohr-Mollerup's Theorem for Higher Order Convex Functions |
| Medium | [electronic resource] / |
| Statement of responsibility, etc. | by Jean-Luc Marichal, Naïm Zenaïdi. |
| 250 ## - EDITION STATEMENT | |
| Edition statement | 1st ed. 2022. |
| 264 #1 - PRODUCTION, PUBLICATION, DISTRIBUTION, MANUFACTURE, AND COPYRIGHT NOTICE | |
| Place of production, publication, distribution, manufacture | Cham : |
| Name of producer, publisher, distributor, manufacturer | Springer International Publishing : |
| -- | Imprint: Springer, |
| Date of production, publication, distribution, manufacture, or copyright notice | 2022. |
| 300 ## - PHYSICAL DESCRIPTION | |
| Extent | XVIII, 323 p. |
| Other physical details | online resource. |
| 336 ## - CONTENT TYPE | |
| Content type term | text |
| Content type code | txt |
| Source | rdacontent |
| 337 ## - MEDIA TYPE | |
| Media type term | computer |
| Media type code | c |
| Source | rdamedia |
| 338 ## - CARRIER TYPE | |
| Carrier type term | online resource |
| Carrier type code | cr |
| Source | rdacarrier |
| 347 ## - DIGITAL FILE CHARACTERISTICS | |
| File type | text file |
| Encoding format | |
| Source | rda |
| 490 1# - SERIES STATEMENT | |
| Series statement | Developments in Mathematics, |
| International Standard Serial Number | 2197-795X ; |
| Volume/sequential designation | 70 |
| 505 0# - FORMATTED CONTENTS NOTE | |
| Formatted contents note | 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. |
| 506 0# - RESTRICTIONS ON ACCESS NOTE | |
| Terms governing access | Open Access |
| 520 ## - SUMMARY, ETC. | |
| Summary, etc. | 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. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name entry element | Special functions. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name entry element | Difference equations. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name entry element | Functional equations. |
| 650 14 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name entry element | Special Functions. |
| 650 24 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name entry element | Difference and Functional Equations. |
| 700 1# - ADDED ENTRY--PERSONAL NAME | |
| Personal name | Zenaïdi, Naïm. |
| Relator term | author. |
| Relationship | aut |
| -- | http://id.loc.gov/vocabulary/relators/aut |
| 710 2# - ADDED ENTRY--CORPORATE NAME | |
| Corporate name or jurisdiction name as entry element | SpringerLink (Online service) |
| 773 0# - HOST ITEM ENTRY | |
| Title | Springer Nature eBook |
| 776 08 - ADDITIONAL PHYSICAL FORM ENTRY | |
| Relationship information | Printed edition: |
| International Standard Book Number | 9783030950873 |
| 776 08 - ADDITIONAL PHYSICAL FORM ENTRY | |
| Relationship information | Printed edition: |
| International Standard Book Number | 9783030950897 |
| 776 08 - ADDITIONAL PHYSICAL FORM ENTRY | |
| Relationship information | Printed edition: |
| International Standard Book Number | 9783030950903 |
| 830 #0 - SERIES ADDED ENTRY--UNIFORM TITLE | |
| Uniform title | Developments in Mathematics, |
| International Standard Serial Number | 2197-795X ; |
| Volume/sequential designation | 70 |
| 856 40 - ELECTRONIC LOCATION AND ACCESS | |
| Uniform Resource Identifier | <a href="https://doi.org/10.1007/978-3-030-95088-0">https://doi.org/10.1007/978-3-030-95088-0</a> |
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| -- | ZDB-2-SMA |
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| -- | ZDB-2-SOB |
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