LEADER 04468nam 22006255 450 001 9910583594703321 005 20251113194550.0 010 $a3-030-95088-3 024 7 $a10.1007/978-3-030-95088-0 035 $a(CKB)5700000000101748 035 $a(MiAaPQ)EBC7041855 035 $a(Au-PeEL)EBL7041855 035 $a(OCoLC)1335127471 035 $a(oapen)https://directory.doabooks.org/handle/20.500.12854/87685 035 $a(PPN)263897478 035 $a(ODN)ODN0010066366 035 $a(oapen)doab87685 035 $a(DE-He213)978-3-030-95088-0 035 $a(EXLCZ)995700000000101748 100 $a20220706d2022 u| 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 12$aA Generalization of Bohr-Mollerup's Theorem for Higher Order Convex Functions /$fby Jean-Luc Marichal, Naïm Zenaïdi 205 $a1st ed. 2022. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2022. 215 $a1 online resource (xviii, 323 pages) 225 1 $aDevelopments in Mathematics,$x2197-795X ;$v70 311 1 $a3-030-95087-5 327 $aPreface -- 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. 330 $aIn 1922, Harald Bohr and Johannes Mollerup established a remarkable characterization of the Euler gamma function using its log-convexity property. A decade later, Emil Artin investigated this result and used it to derive the basic properties of the gamma function using elementary methods of the calculus. Bohr-Mollerup's theorem was then adopted by Nicolas Bourbaki as the starting point for his exposition of the gamma function. This open access book develops a far-reaching generalization of Bohr-Mollerup's theorem to higher order convex functions, along lines initiated by Wolfgang Krull, Roger Webster, and some others but going considerably further than past work. In particular, this generalization shows using elementary techniques that a very rich spectrum of functions satisfy analogues of several classical properties of the gamma function, including Bohr-Mollerup's theorem itself, Euler's reflection formula, Gauss' multiplication theorem, Stirling's formula, and Weierstrass' canonical factorization. The scope of the theory developed in this work is illustrated through various examples, ranging from the gamma function itself and its variants and generalizations (q-gamma, polygamma, multiple gamma functions) to important special functions such as the Hurwitz zeta function and the generalized Stieltjes constants. This volume is also an opportunity to honor the 100th anniversary of Bohr-Mollerup's theorem and to spark the interest of a large number of researchers in this beautiful theory. 410 0$aDevelopments in Mathematics,$x2197-795X ;$v70 606 $aSpecial functions 606 $aDifference equations 606 $aFunctional equations 606 $aSpecial Functions 606 $aDifference and Functional Equations 615 0$aSpecial functions. 615 0$aDifference equations. 615 0$aFunctional equations. 615 14$aSpecial Functions. 615 24$aDifference and Functional Equations. 676 $a515.5 686 $aMAT034000$2bisacsh 700 $aMarichal$b Jean-Luc$01255007 701 $aZenaïdi$b Naïm$01255008 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910583594703321 996 $aGeneralization of Bohr-Mollerup's Theorem for Higher Order Convex Functions$94161042 997 $aUNINA