Zeta And Q Zeta Functions And Associated Series And Integrals

Author : H. M. Srivastava,Junesang Choi
Publisher : Elsevier
Page : 675 pages
File Size : 47,7 Mb
Release : 2011-10-25
Category : Mathematics
ISBN : 9780123852182

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Zeta and Q-Zeta Functions and Associated Series and Integrals by H. M. Srivastava,Junesang Choi Pdf

Zeta and q-Zeta Functions and Associated Series and Integrals is a thoroughly revised, enlarged and updated version of Series Associated with the Zeta and Related Functions. Many of the chapters and sections of the book have been significantly modified or rewritten, and a new chapter on the theory and applications of the basic (or q-) extensions of various special functions is included. This book will be invaluable because it covers not only detailed and systematic presentations of the theory and applications of the various methods and techniques used in dealing with many different classes of series and integrals associated with the Zeta and related functions, but stimulating historical accounts of a large number of problems and well-classified tables of series and integrals. Detailed and systematic presentations of the theory and applications of the various methods and techniques used in dealing with many different classes of series and integrals associated with the Zeta and related functions

Author : Hari M. Srivastava,Junesang Choi
Publisher : Springer Science & Business Media
Page : 408 pages
File Size : 42,7 Mb
Release : 2001
Category : Mathematics
ISBN : 0792370546

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Series Associated With the Zeta and Related Functions by Hari M. Srivastava,Junesang Choi Pdf

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.

Author : Jianqiang Zhao
Publisher : World Scientific
Page : 620 pages
File Size : 53,8 Mb
Release : 2016-03-07
Category : Mathematics
ISBN : 9789814689410

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Multiple Zeta Functions, Multiple Polylogarithms and Their Special Values by Jianqiang Zhao Pdf

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. Contents:Multiple Zeta FunctionsMultiple Polylogarithms (MPLs)Multiple Zeta Values (MZVs)Drinfeld Associator and Single-Valued MZVsMultiple Zeta Value IdentitiesSymmetrized Multiple Zeta Values (SMZVs)Multiple Harmonic Sums (MHSs) and Alternating VersionFinite Multiple Zeta Values and Finite Euler Sumsq-Analogs of Multiple Harmonic (Star) Sums Readership: Advanced undergraduates and graduate students in mathematics, mathematicians interested in multiple zeta values. Key Features:For the first time, a detailed explanation of the theory of multiple zeta values is given in book form along with numerous illustrations in explicit examplesThe book provides for the first time a comprehensive introduction to multiple polylogarithms and their special values at roots of unity, from the basic definitions to the more advanced topics in current active researchThe book contains a few quite intriguing results relating the special values of multiple zeta functions and multiple polylogarithms to other branches of mathematics and physics, such as knot theory and the theory of motivesMany exercises contain supplementary materials which deepens the reader's understanding of the main text

Author : Hari M. Srivastava,Junesang Choi
Publisher : Springer
Page : 0 pages
File Size : 47,5 Mb
Release : 2001
Category : Mathematics
ISBN : 9401596727

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Series Associated with the Zeta and Related Functions by Hari M. Srivastava,Junesang Choi Pdf

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.

Author : Marcus du Sautoy,Luke Woodward
Publisher : Springer Science & Business Media
Page : 217 pages
File Size : 55,9 Mb
Release : 2008
Category : Mathematics
ISBN : 9783540747017

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Zeta Functions of Groups and Rings by Marcus du Sautoy,Luke Woodward Pdf

Zeta functions have been a powerful tool in mathematics over the last two centuries. This book considers a new class of non-commutative zeta functions which encode the structure of the subgroup lattice in infinite groups. The book explores the analytic behaviour of these functions together with an investigation of functional equations. Many important examples of zeta functions are calculated and recorded providing an important data base of explicit examples and methods for calculation.

Author : Shigeru Kanemitsu,Haruo Tsukada
Publisher : World Scientific
Page : 316 pages
File Size : 43,9 Mb
Release : 2015
Category : Mathematics
ISBN : 9789814449625

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Contributions to the Theory of Zeta-Functions by Shigeru Kanemitsu,Haruo Tsukada Pdf

This volume provides a systematic survey of almost all the equivalent assertions to the functional equations - zeta symmetry - which zeta-functions satisfy, thus streamlining previously published results on zeta-functions. The equivalent relations are given in the form of modular relations in Fox H-function series, which at present include all that have been considered as candidates for ingredients of a series. The results are presented in a clear and simple manner for readers to readily apply without much knowledge of zeta-functions. This volume aims to keep a record of the 150-year-old heritage starting from Riemann on zeta-functions, which are ubiquitous in all mathematical sciences, wherever there is a notion of the norm. It provides almost all possible equivalent relations to the zeta-functions without requiring a reader's deep knowledge on their definitions. This can be an ideal reference book for those studying zeta-functions.

Author : H. M. Srivastava
Publisher : MDPI
Page : 510 pages
File Size : 43,9 Mb
Release : 2019-11-20
Category : Technology & Engineering
ISBN : 9783039216185

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Integral Transforms and Operational Calculus by H. M. Srivastava Pdf

Researches and investigations involving the theory and applications of integral transforms and operational calculus are remarkably wide-spread in many diverse areas of the mathematical, physical, chemical, engineering and statistical sciences. This Special Issue contains a total of 36 carefully-selected and peer-reviewed articles which are authored by established researchers from many countries. Included in this Special Issue are review, expository and original research articles dealing with the recent advances on the topics of integral transforms and operational calculus as well as their multidisciplinary applications

Author : Antanas Laurincikas,Ramunas Garunkstis
Publisher : Springer Science & Business Media
Page : 192 pages
File Size : 49,6 Mb
Release : 2013-12-11
Category : Mathematics
ISBN : 9789401764018

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The Lerch zeta-function by Antanas Laurincikas,Ramunas Garunkstis Pdf

The Lerch zeta-function is the first monograph on this topic, which is a generalization of the classic Riemann, and Hurwitz zeta-functions. Although analytic results have been presented previously in various monographs on zeta-functions, this is the first book containing both analytic and probability theory of Lerch zeta-functions. The book starts with classical analytical theory (Euler gamma-functions, functional equation, mean square). The majority of the presented results are new: on approximate functional equations and its applications and on zero distribution (zero-free regions, number of nontrivial zeros etc). Special attention is given to limit theorems in the sense of the weak convergence of probability measures for the Lerch zeta-function. From limit theorems in the space of analytic functions the universitality and functional independence is derived. In this respect the book continues the research of the first author presented in the monograph Limit Theorems for the Riemann zeta-function. This book will be useful to researchers and graduate students working in analytic and probabilistic number theory, and can also be used as a textbook for postgraduate students.

Author : Gradimir V. Milovanović,Michael Th. Rassias
Publisher : Springer
Page : 880 pages
File Size : 49,6 Mb
Release : 2014-07-08
Category : Mathematics
ISBN : 9781493902583

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Analytic Number Theory, Approximation Theory, and Special Functions by Gradimir V. Milovanović,Michael Th. Rassias Pdf

This book, in honor of Hari M. Srivastava, discusses essential developments in mathematical research in a variety of problems. It contains thirty-five articles, written by eminent scientists from the international mathematical community, including both research and survey works. Subjects covered include analytic number theory, combinatorics, special sequences of numbers and polynomials, analytic inequalities and applications, approximation of functions and quadratures, orthogonality and special and complex functions. The mathematical results and open problems discussed in this book are presented in a simple and self-contained manner. The book contains an overview of old and new results, methods, and theories toward the solution of longstanding problems in a wide scientific field, as well as new results in rapidly progressing areas of research. The book will be useful for researchers and graduate students in the fields of mathematics, physics and other computational and applied sciences.

Author : Živorad Tomovski,Delčo Leškovski,Stefan Gerhold
Publisher : Springer Nature
Page : 167 pages
File Size : 46,9 Mb
Release : 2021-11-15
Category : Mathematics
ISBN : 9783030848170

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Generalized Mathieu Series by Živorad Tomovski,Delčo Leškovski,Stefan Gerhold Pdf

The Mathieu series is a functional series introduced by Émile Léonard Mathieu for the purposes of his research on the elasticity of solid bodies. Bounds for this series are needed for solving biharmonic equations in a rectangular domain. In addition to Tomovski and his coauthors, Pogany, Cerone, H. M. Srivastava, J. Choi, etc. are some of the known authors who published results concerning the Mathieu series, its generalizations and their alternating variants. Applications of these results are given in classical, harmonic and numerical analysis, analytical number theory, special functions, mathematical physics, probability, quantum field theory, quantum physics, etc. Integral representations, analytical inequalities, asymptotic expansions and behaviors of some classes of Mathieu series are presented in this book. A systematic study of probability density functions and probability distributions associated with the Mathieu series, its generalizations and Planck’s distribution is also presented. The book is addressed at graduate and PhD students and researchers in mathematics and physics who are interested in special functions, inequalities and probability distributions.

Author : Safoura Rezaei Aderyani
Publisher : Springer Nature
Page : 580 pages
File Size : 50,9 Mb
Release : 2024-06-01
Category : Electronic
ISBN : 9783031555640

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Towards Ulam Type Multi Stability Analysis by Safoura Rezaei Aderyani Pdf

Author : André Voros
Publisher : Springer Science & Business Media
Page : 163 pages
File Size : 51,5 Mb
Release : 2009-11-21
Category : Mathematics
ISBN : 9783642052033

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Zeta Functions over Zeros of Zeta Functions by André Voros Pdf

In this text, the famous zeros of the Riemann zeta function and its generalizations (L-functions, Dedekind and Selberg zeta functions)are analyzed through several zeta functions built over those zeros.

Author : Robert Spira
Publisher : Unknown
Page : 424 pages
File Size : 47,8 Mb
Release : 1999
Category : Functions, Zeta
ISBN : CORNELL:31924086163080

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History of Zeta Functions by Robert Spira Pdf

Author : Athanassios S. Fokas,Jonatan Lenells
Publisher : American Mathematical Society
Page : 114 pages
File Size : 51,7 Mb
Release : 2022-02-02
Category : Mathematics
ISBN : 9781470450984

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On the Asymptotics to all Orders of the Riemann Zeta Function and of a Two-Parameter Generalization of the Riemann Zeta Function by Athanassios S. Fokas,Jonatan Lenells Pdf

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Author : Themistocles M. Rassias
Publisher : Springer Nature
Page : 546 pages
File Size : 46,7 Mb
Release : 2021-07-21
Category : Mathematics
ISBN : 9783030606220

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Approximation Theory and Analytic Inequalities by Themistocles M. Rassias Pdf

This contributed volume focuses on various important areas of mathematics in which approximation methods play an essential role. It features cutting-edge research on a wide spectrum of analytic inequalities with emphasis on differential and integral inequalities in the spirit of functional analysis, operator theory, nonlinear analysis, variational calculus, featuring a plethora of applications, making this work a valuable resource. The reader will be exposed to convexity theory, polynomial inequalities, extremal problems, prediction theory, fixed point theory for operators, PDEs, fractional integral inequalities, multidimensional numerical integration, Gauss–Jacobi and Hermite–Hadamard type inequalities, Hilbert-type inequalities, and Ulam’s stability of functional equations. Contributions have been written by eminent researchers, providing up-to-date information and several results which may be useful to a wide readership including graduate students and researchers working in mathematics, physics, economics, operational research, and their interconnections.