Special Values Of The Hypergeometric Series
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Special Values Of The Hypergeometric Series
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Author : Akihito Ebisu
language : en
Publisher:
Release Date : 2017
Special Values Of The Hypergeometric Series written by Akihito Ebisu and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017 with Cohen-Macaulay modules categories.
In this paper, the author presents a new method for finding identities for hypergeoemtric series, such as the (Gauss) hypergeometric series, the generalized hypergeometric series and the Appell-Lauricella hypergeometric series. Furthermore, using this method, the author gets identities for the hypergeometric series F(a,b;c;x) and shows that values of F(a,b;c;x) at some points x can be expressed in terms of gamma functions, together with certain elementary functions. The author tabulates the values of F(a,b;c;x) that can be obtained with this method and finds that this set includes almost all previously known values and many previously unknown values
Special Functions
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Author : George E. Andrews
language : en
Publisher: Cambridge University Press
Release Date : 1999
Special Functions written by George E. Andrews and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999 with Mathematics categories.
An overview of special functions, focusing on the hypergeometric functions and the associated hypergeometric series.
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Author : George E. Andrews
language : en
Publisher: 清华大学出版社有限公司
Release Date : 2004
written by George E. Andrews and has been published by 清华大学出版社有限公司 this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with Functions, Special categories.
Current Topics In Analytic Function Theory
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Author : Shigeyoshi Owa
language : en
Publisher: World Scientific
Release Date : 1992-12-31
Current Topics In Analytic Function Theory written by Shigeyoshi Owa and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992-12-31 with Mathematics categories.
This volume is a collection of research-and-survey articles by eminent and active workers around the world on the various areas of current research in the theory of analytic functions.Many of these articles emerged essentially from the proceedings of, and various deliberations at, three recent conferences in Japan and Korea: An International Seminar on Current Topics in Univalent Functions and Their Applications which was held in August 1990, in conjunction with the International Congress of Mathematicians at Kyoto, at Kinki University in Osaka; An International Seminar on Univalent Functions, Fractional Calculus, and Their Applications which was held in October 1990 at Fukuoka University; and also the Japan-Korea Symposium on Univalent Functions which was held in January 1991 at Gyeongsang National University in Chinju.
Periods And Special Functions In Transcendence
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Author : Paula B Tretkoff
language : en
Publisher: World Scientific
Release Date : 2017-05-04
Periods And Special Functions In Transcendence written by Paula B Tretkoff and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-05-04 with Mathematics categories.
'The book is mainly addressed to the non-expert reader, in that it assumes only a little background in complex analysis and algebraic geometry, but no previous knowledge in transcendental number theory is required. The technical language is introduced smoothly, and illustrative examples are provided where appropriate … The book is carefully written, and the relevant literature is provided in the list of references. 'Mathematical Reviews ClippingsThis book gives an introduction to some central results in transcendental number theory with application to periods and special values of modular and hypergeometric functions. It also includes related results on Calabi-Yau manifolds. Most of the material is based on the author's own research and appears for the first time in book form. It is presented with minimal of technical language and no background in number theory is needed. In addition, except the last chapter, all chapters include exercises suitable for graduate students. It is a nice book for graduate students and researchers interested in transcendence.
2017 Matrix Annals
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Author : Jan de Gier
language : en
Publisher: Springer
Release Date : 2019-03-13
2017 Matrix Annals written by Jan de Gier and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-03-13 with Mathematics categories.
MATRIX is Australia’s international and residential mathematical research institute. It facilitates new collaborations and mathematical advances through intensive residential research programs, each 1-4 weeks in duration. This book is a scientific record of the eight programs held at MATRIX in its second year, 2017: - Hypergeometric Motives and Calabi–Yau Differential Equations - Computational Inverse Problems - Integrability in Low-Dimensional Quantum Systems - Elliptic Partial Differential Equations of Second Order: Celebrating 40 Years of Gilbarg and Trudinger’s Book - Combinatorics, Statistical Mechanics, and Conformal Field Theory - Mathematics of Risk - Tutte Centenary Retreat - Geometric R-Matrices: from Geometry to Probability The articles are grouped into peer-reviewed contributions and other contributions. The peer-reviewed articles present original results or reviews on a topic related to the MATRIX program; the remaining contributions are predominantly lecture notes or short articles based on talks or activities at MATRIX.
From Operator Theory To Orthogonal Polynomials Combinatorics And Number Theory
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Author : Fritz Gesztesy
language : en
Publisher: Springer Nature
Release Date : 2021-11-11
From Operator Theory To Orthogonal Polynomials Combinatorics And Number Theory written by Fritz Gesztesy and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-11-11 with Mathematics categories.
The main topics of this volume, dedicated to Lance Littlejohn, are operator and spectral theory, orthogonal polynomials, combinatorics, number theory, and the various interplays of these subjects. Although the event, originally scheduled as the Baylor Analysis Fest, had to be postponed due to the pandemic, scholars from around the globe have contributed research in a broad range of mathematical fields. The collection will be of interest to both graduate students and professional mathematicians. Contributors are: G.E. Andrews, B.M. Brown, D. Damanik, M.L. Dawsey, W.D. Evans, J. Fillman, D. Frymark, A.G. García, L.G. Garza, F. Gesztesy, D. Gómez-Ullate, Y. Grandati, F.A. Grünbaum, S. Guo, M. Hunziker, A. Iserles, T.F. Jones, K. Kirsten, Y. Lee, C. Liaw, F. Marcellán, C. Markett, A. Martinez-Finkelshtein, D. McCarthy, R. Milson, D. Mitrea, I. Mitrea, M. Mitrea, G. Novello, D. Ong, K. Ono, J.L. Padgett, M.M.M. Pang, T. Poe, A. Sri Ranga, K. Schiefermayr, Q. Sheng, B. Simanek, J. Stanfill, L. Velázquez, M. Webb, J. Wilkening, I.G. Wood, M. Zinchenko.
Series Associated With The Zeta And Related Functions
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Author : Hari M. Srivastava
language : en
Publisher: Springer Science & Business Media
Release Date : 2001
Series Associated With The Zeta And Related Functions written by Hari M. Srivastava and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001 with Mathematics categories.
In recent years there has been an increasing interest in problems involving closed form evaluations of (and representations of the Riemann Zeta function at positive integer arguments as) various families of series associated with the Riemann Zeta function ((s), the Hurwitz Zeta function ((s,a), and their such extensions and generalizations as (for example) Lerch's transcendent (or the Hurwitz-Lerch Zeta function) iI>(z, s, a). Some of these developments have apparently stemmed from an over two-century-old theorem of Christian Goldbach (1690-1764), which was stated in a letter dated 1729 from Goldbach to Daniel Bernoulli (1700-1782), from recent rediscoveries of a fairly rapidly convergent series representation for ((3), which is actually contained in a 1772 paper by Leonhard Euler (1707-1783), and from another known series representation for ((3), which was used by Roger Apery (1916-1994) in 1978 in his celebrated proof of the irrationality of ((3). This book is motivated essentially by the fact that the theories and applications of the various methods and techniques used in dealing with many different families of series associated with the Riemann Zeta function and its aforementioned relatives are to be found so far only"in widely scattered journal articles. Thus our systematic (and unified) presentation of these results on the evaluation and representation of the Zeta and related functions is expected to fill a conspicuous gap in the existing books dealing exclusively with these Zeta functions.
Multiple Zeta Functions Multiple Polylogarithms And Their Special Values
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Author : Jianqiang Zhao
language : en
Publisher: World Scientific
Release Date : 2016-03-07
Multiple Zeta Functions Multiple Polylogarithms And Their Special Values written by Jianqiang Zhao and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-03-07 with Mathematics categories.
This is the first introductory book on multiple zeta functions and multiple polylogarithms which are the generalizations of the Riemann zeta function and the classical polylogarithms, respectively, to the multiple variable setting. It contains all the basic concepts and the important properties of these functions and their special values. This book is aimed at graduate students, mathematicians and physicists who are interested in this current active area of research.The book will provide a detailed and comprehensive introduction to these objects, their fascinating properties and interesting relations to other mathematical subjects, and various generalizations such as their q-analogs and their finite versions (by taking partial sums modulo suitable prime powers). Historical notes and exercises are provided at the end of each chapter.
Linear Differential Equations In The Complex Domain
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Author : Yoshishige Haraoka
language : en
Publisher: Springer Nature
Release Date : 2020-11-16
Linear Differential Equations In The Complex Domain written by Yoshishige Haraoka and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-11-16 with Mathematics categories.
This book provides a detailed introduction to recent developments in the theory of linear differential systems and integrable total differential systems. Starting from the basic theory of linear ordinary differential equations and integrable systems, it proceeds to describe Katz theory and its applications, extending it to the case of several variables. In addition, connection problems, deformation theory, and the theory of integral representations are comprehensively covered. Complete proofs are given, offering the reader a precise account of the classical and modern theory of linear differential equations in the complex domain, including an exposition of Pfaffian systems and their monodromy problems. The prerequisites are a course in complex analysis and the basics of differential equations, topology and differential geometry. This book will be useful for graduate students, specialists in differential equations, and for non-specialists who want to use differential equations.