A Generalization of Bohr-Mollerup's Theorem for Higher Order Convex Functions PDF Download
Are you looking for read ebook online? Search for your book and save it on your Kindle device, PC, phones or tablets. Download A Generalization of Bohr-Mollerup's Theorem for Higher Order Convex Functions PDF full book. Access full book title A Generalization of Bohr-Mollerup's Theorem for Higher Order Convex Functions by Jean-Luc Marichal. Download full books in PDF and EPUB format.
Author: Jean-Luc Marichal Publisher: Springer Nature ISBN: 3030950883 Category : Mathematics Languages : en Pages : 325
Book Description
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.
Author: Bob Levy Publisher: Routledge ISBN: 0429013434 Category : Art Languages : en Pages : 471
Book Description
Development is a large and central part of the American TV industry, and yet the details of how it works – who makes development decisions and why, where ideas for new shows come from, even basics like the differences between what TV studios and TV networks do – remain elusive to many. In this book, lecturer and acclaimed television producer Bob Levy offers a detailed introduction to television development, the process by which the Hollywood TV industry creates new scripted series. Written both for students and industry professionals, Television Development serves as a comprehensive introduction to all facets of the development process: the terminology, timelines, personnel and industrial processes that take a new TV project from idea to pitch to script to pilot to series. In addition to describing these processes, Levy also examines creative strategies for successful development, and teaches readers how to apply these strategies to their own careers and speak the language of development across all forms of visual storytelling. Written by the renowned producer responsible for developing and executive producing Gossip Girl and Pretty Little Liars, Television Development is an essential starting point for students, executives, agents, producers, directors and writers to learn how new series are created. Accompanying online material includes sample pitches, pilot scripts, and other development documents. A companion website for the book is available here: https://www.tvboblevy.com/
Author: Jean-Luc Marichal Publisher: Springer Nature ISBN: 3030950883 Category : Mathematics Languages : en Pages : 325
Book Description
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.
Author: Stephen Seligman Publisher: Routledge ISBN: 113696505X Category : Psychology Languages : en Pages : 374
Book Description
The recent explosion of new research about infants, parental care, and infant-parent relationships has shown conclusively that human relationships are central motivators and organizers in development. Relationships in Development examines the practical implications for dynamic psychotherapy with both adults and children, especially following trauma. Stephen Seligman offers engaging examples of infant-parent interactions as well as of psychotherapeutic process. He traces the place of childhood and child development in psychoanalysis from Freud onward, showing how different images about babies evolved and influenced analytic theory and practice. Relationships in Development offers a new integration of ideas that updates established psychoanalytic models in a new context: "Relational-developmental psychoanalysis." Seligman integrates four crucial domains: Infancy Research, including attachment theory and research Developmental Psychoanalysis Relational/intersubjective Psychoanalysis Classical Freudian, Kleinian, and Object Relations theories (including Winnicott). An array of specific sources are included: developmental neuroscience, attachment theory and research, studies of emotion, trauma and infant-parent interaction, and nonlinear dynamic systems theories. Although new psychoanalytic approaches are featured, the classical theories are not neglected, including the Freudian, Kleinian, Winnicottian, and Ego Psychology orientations. Seligman links current knowledge about early experiences and how they shape later development with the traditional psychoanalytic attention to the irrational, unconscious, turbulent, and unknowable aspects of the mind and human interaction. These different fields are taken together to offer an open and flexible approach to psychodynamic therapy with a variety of patients in different socioeconomic and cultural situations. Relationships in Development will appeal to psychoanalysts, psychoanalytic psychotherapists, and graduate students in psychology, social work, and psychotherapy. The fundamental issues and implications presented will also be of great importance to the wider psychodynamic and psychotherapeutic communities.
Author: Artin Goncu Publisher: Psychology Press ISBN: 1135592438 Category : Family & Relationships Languages : en Pages : 311
Book Description
Children's play is a universal human activity, and one that serves a significant purpose in personal development.Throughout this volume, which is an extension of the 33rd Annual Meeting of the Jean Piaget Society, the editors and contributors explore assumptions about play and its status as a unique and universal activity in humans.As a whole, Play
Author: Gérard Roland Publisher: Routledge ISBN: 1315510553 Category : Business & Economics Languages : en Pages : 1011
Book Description
Gerard Roland's new text, Development Economics, is the first undergraduate text to recognize the role of institutions in understanding development and growth. Through a series of chapters devoted to specific sets of institutions, Roland examines the effects of institutions on growth, property rights, market development, and the delivery of public goods and services and focuses. With the most comprehensive and up to date treatment of institutions on development, Roland explores the important questions of why some countries develop faster than others and why some fail while others are successful.
Author: Roger Levermore Publisher: Springer ISBN: 0230584403 Category : Social Science Languages : en Pages : 296
Book Description
Investigating the capacity of sport to act both as a conduit for traditional development assistance activities and as an agent for change in its own right, this book argues that sport can contribute to the development process, particularly where traditional development approaches have difficulty in engaging with communities.
Author: E. Sahle Publisher: Springer ISBN: 0230274862 Category : Political Science Languages : en Pages : 285
Book Description
The book examines how hegemonic development ideas and practices emerged in the context of the changing world order post-1945 and how this transformation was characterized by neoliberalism and securitization of development and security. Sahle also explores the rise of China and the start of Obama's presidency.
Author: M. M. Shirley Publisher: Edward Elgar Publishing ISBN: 1848443994 Category : Business & Economics Languages : en Pages : 241
Book Description
Both economic research and the history of foreign aid suggest that the largest barriers to development arise from a society's institutions - its norms and rules. This book explains how institutions drive economic development. It provides numerous examples to illustrate the complex, interlocking, and persistent nature of real world rules and norms.
Author: Jean-Luc Marichal
Author: Bob Levy
Author: Jean-Luc Marichal
Author: Stephen Seligman
Author: Artin Goncu
Author: Gérard Roland
Author: Roger Levermore
Author: E. Sahle
Author: M. M. Shirley
Author: Brett Slatkin
Author: Stanley L. Engerman