說明 
xviii, 323 pages : illustrations ; 25 cm 

text txt rdacontent 

unmediated n rdamedia 

volume nc rdacarrier 
系列 
Developments in mathematics ; volume 70 

Developments in mathematics ; v. 70

附註 
Includes bibliographical references and index 

In 1922, Harald Bohr and Johannes Mollerup established a remarkable characterization of the Euler gamma function using its logconvexity 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. BohrMollerup'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 farreaching generalization of BohrMollerup'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 BohrMollerup'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 (qgamma, 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 BohrMollerup's theorem and to spark the interest of a large number of researchers in this beautiful theory 

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 loggamma type functions  Chapter 6. Asymptotic analysis  Chapter 7. Derivatives of multiple loggamma 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 loggamma type functions  Chapter 12. Further examples  Chapter 13. Conclusion  A. Higher order convexity properties  B. On KrullWebster'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 

Current copyright fee: GBP19.00 42\0. Uk 
主題 
Convex functions


Gamma functions


Convex functions. fast (OCoLC)fst00877260


Gamma functions. fast (OCoLC)fst00937592

Alt Author 
Zenaidi, Naim, author

