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001431465 020__ $$a9783030950880$$q(electronic bk.)
001431465 020__ $$a3030950883$$q(electronic bk.)
001431465 020__ $$z9783030950873
001431465 0247_ $$a10.1007/978-3-030-95088-0$$2doi
001431465 035__ $$aSP(OCoLC)1335127471
001431465 040__ $$aGW5XE$$beng$$erda$$epn$$cGW5XE$$dEBLCP$$dOCLCF$$dOCLCQ
001431465 049__ $$aISEA
001431465 050_4 $$aQA331.5
001431465 08204 $$a515/.8$$223/eng/20220712
001431465 1001_ $$aMarichal, Jean-Luc,$$eauthor.
001431465 24512 $$aA generalization of Bohr-Mollerup's theorem for higher order convex functions /$$cJean-Luc Marichal, Naïm Zenaïdi.
001431465 264_1 $$aCham :$$bSpringer,$$c[2022]
001431465 264_4 $$c©2022
001431465 300__ $$a1 online resource (xviii, 323 pages).
001431465 336__ $$atext$$btxt$$2rdacontent
001431465 337__ $$acomputer$$bc$$2rdamedia
001431465 338__ $$aonline resource$$bcr$$2rdacarrier
001431465 4901_ $$aDevelopments in mathematics,$$x2197-795X ;$$vvolume 70
001431465 504__ $$aIncludes bibliographical references and index.
001431465 5050_ $$aPreface -- List of main symbols -- Table of contents -- Chapter 1. Introduction -- Chapter 2. Preliminaries -- Chapter 3. Uniqueness and existence results -- Chapter 4. Interpretations of the asymptotic conditions -- Chapter 5. Multiple log-gamma type functions -- Chapter 6. Asymptotic analysis -- Chapter 7. Derivatives of multiple log-gamma type functions -- Chapter 8. Further results -- Chapter 9. Summary of the main results -- Chapter 10. Applications to some standard special functions -- Chapter 11. Definining new log-gamma type functions -- Chapter 12. Further examples -- Chapter 13. Conclusion -- A. Higher order convexity properties -- B. On Krull-Webster's asymptotic condition -- C. On a question raised by Webster -- D. Asymptotic behaviors and bracketing -- E. Generalized Webster's inequality -- F. On the differentiability of \sigma_g -- Bibliography -- Analogues of properties of the gamma function -- Index.
001431465 5060_ $$aOpen access$$5GW5XE
001431465 520__ $$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.
001431465 588__ $$aOnline resource; title from PDF title page (SpringerLink, viewed July 12, 2022).
001431465 650_0 $$aConvex functions.
001431465 650_0 $$aGamma functions.
001431465 655_0 $$aElectronic books.
001431465 7001_ $$aZenaïdi, Naïm,$$eauthor.
001431465 830_0 $$aDevelopments in mathematics ;$$vv. 70.$$x2197-795X
001431465 852__ $$bebk
001431465 85640 $$3Springer Nature$$uhttps://link.springer.com/10.1007/978-3-030-95088-0$$zOnline Access$$91397441.2
001431465 909CO $$ooai:library.usi.edu:1431465$$pGLOBAL_SET
001431465 980__ $$aBIB
001431465 980__ $$aEBOOK
001431465 982__ $$aEbook
001431465 983__ $$aOnline
001431465 994__ $$a92$$bISE