04601nam 22007093 450 99648315360331620220921220714.03-030-95088-3(CKB)5700000000101748(MiAaPQ)EBC7041855(Au-PeEL)EBL7041855(OCoLC)1335127471(oapen)https://directory.doabooks.org/handle/20.500.12854/87685(PPN)263897478(EXLCZ)99570000000010174820220919d2022 fy 0engurcnu||||||||txtrdacontentcrdamediacrrdacarrierA generalization of Bohr-Mollerup's theorem for higher order convex functions /Jean-Luc Marichal, Naïm ZenaïdiChamSpringer Nature2022Cham :Springer International Publishing AG,2022.©2022.1 online resource (xviii, 323 pages)Developments in mathematicsv.703-030-95087-5 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. Defining 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 IndexIn 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.Developments in mathematics70.Convex functionsGamma functionsDifference EquationHigher Order ConvexityBohr-Mollerup's TheoremPrincipal Indefinite SumsGauss' LimitEuler Product FormRaabe's FormulaBinet's FunctionStirling's FormulaEuler's Infinite ProductEuler's Reflection FormulaWeierstrass' Infinite ProductGauss Multiplication FormulaEuler's ConstantGamma FunctionPolygamma FunctionsHurwitz Zeta FunctionGeneralized Stieltjes ConstantsConvex functions.Gamma functions.Marichal Jean-Luc1255007Zenaïdi Naïm1255008MiAaPQMiAaPQMiAaPQBOOK996483153603316A generalization of Bohr-Mollerup's theorem for higher order convex functions2909870UNISA03925nam 2200661 a 450 991078005050332120230421041439.01-282-75197-297866127519741-4008-2136-31-4008-1379-410.1515/9781400821365(CKB)111056486503546(EBL)581667(OCoLC)700688709(SSID)ssj0000158465(PQKBManifestationID)11155351(PQKBTitleCode)TC0000158465(PQKBWorkID)10149757(PQKB)10036123(MiAaPQ)EBC581667(OCoLC)51575505(MdBmJHUP)muse35946(DE-B1597)446087(OCoLC)979954260(DE-B1597)9781400821365(Au-PeEL)EBL581667(CaPaEBR)ebr10035790(CaONFJC)MIL275197(EXLCZ)9911105648650354619940314d1994 uy 0engurnn#---|u||utxtccrFreud's wishful dream book[electronic resource] /Alexander WelshCourse BookPrinceton, N.J. Princeton University Pressc19941 online resource (158 p.)Description based upon print version of record.0-691-03718-3 Includes bibliographical references (p. 139-145).Front matter --CONTENTS --PREFACE --CHAPTER ONE. "A Dream Is the Fulfilment of a Wish" --CHAPTER TWO. "Dreams Really Have a Secret Meaning" --CHAPTER THREE. "So Far as I Knew, I Was Not an Ambitious Man" --CHAPTER FOUR. "It Had Been Possible to Hoodwink the Censorship" --CHAPTER FIVE. "The Only Villain among the Crowd of Noble Characters" --INDEX OF WORKS CITEDAlthough it is customary to credit Freud's self-analysis, it may be more accurate, Alexander Welsh argues, to say that psychoanalysis began when The Interpretation of Dreams was published in the last weeks of the nineteenth century. Only by going public with his theory--that dreams manifest hidden wishes--did Freud establish a position to defend and embark upon a career. That position and career have been among the most influential in this century. In August 1899, Freud wrote to Wilhelm Fliess of the dream book in terms reminiscent of Dante's Inferno. Beginning from a dark wood, this modern journey features "a concealed pass though which I lead the reader--my specimen dream with its peculiarities, details, indiscretions, bad jokes--and then suddenly the high ground and the view and the question, Which way do you wish to go now?" Physician that he is, Freud appoints himself guide rather than hero, yet the way "you" wish to go is very much his prescribed way. In Welsh's book, readers are invited on Freud's journey, to pause at each concealed pass in his seminal work and ask where the guide is taking them and why. Along the way, Welsh shows how Freud's arbitrary turnings are themselves wishful, intended to persuade by pleasing the reader and author alike; that his interest in secrets and his self-proclaimed modest ambition are products of their time; and that the book may best be read as a romance or serial comedy. "Some of the humor throughout," Welsh notes, "can only be understood as a particular kind of fine performance." Welsh offers the first critical overview of the argument in Freud's masterpiece and of the author who presents himself as guide.Dream interpretationPsychoanalysisDream interpretation.Psychoanalysis.154.6/34Welsh Alexander163690MiAaPQMiAaPQMiAaPQBOOK9910780050503321Freud's wishful dream book3674466UNINA