# Zeta And Q Zeta Functions And Associated Series And Integrals

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### Zeta and Q Zeta Functions and Associated Series and Integrals

Author | : H. M. Srivastava,Junesang Choi |

Publsiher | : Elsevier |

Total Pages | : 675 |

Release | : 2011-10-25 |

Genre | : Mathematics |

ISBN | : 9780123852182 |

**Download Zeta and Q Zeta Functions and Associated Series and Integrals Book in PDF, Epub and Kindle**

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

### Zeta and q Zeta Functions and Associated Series and Integrals

Author | : Hari M Srivastava,Junesang Choi |

Publsiher | : Elsevier |

Total Pages | : 675 |

Release | : 2011-10-11 |

Genre | : Mathematics |

ISBN | : 9780123852199 |

**Download Zeta and q Zeta Functions and Associated Series and Integrals Book in PDF, Epub and Kindle**

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

### Series Associated With the Zeta and Related Functions

Author | : Hari M. Srivastava,Junesang Choi |

Publsiher | : Springer Science & Business Media |

Total Pages | : 408 |

Release | : 2001 |

Genre | : Mathematics |

ISBN | : 0792370546 |

**Download Series Associated With the Zeta and Related Functions Book in PDF, Epub and Kindle**

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

Author | : Jianqiang Zhao |

Publsiher | : World Scientific |

Total Pages | : 618 |

Release | : 2016-03-07 |

Genre | : Mathematics |

ISBN | : 9789814689410 |

**Download Multiple Zeta Functions Multiple Polylogarithms And Their Special Values Book in PDF, Epub and Kindle**

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.

### Series Associated with the Zeta and Related Functions

Author | : Hari M. Srivastava,Junesang Choi |

Publsiher | : Springer |

Total Pages | : 0 |

Release | : 2001 |

Genre | : Mathematics |

ISBN | : 9401596727 |

**Download Series Associated with the Zeta and Related Functions Book in PDF, Epub and Kindle**

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.

### Zeta Functions of Groups and Rings

Author | : Marcus du Sautoy,Luke Woodward |

Publsiher | : Springer Science & Business Media |

Total Pages | : 217 |

Release | : 2008 |

Genre | : Mathematics |

ISBN | : 9783540747017 |

**Download Zeta Functions of Groups and Rings Book in PDF, Epub and Kindle**

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.

### The Lerch zeta function

Author | : Antanas Laurincikas,Ramunas Garunkstis |

Publsiher | : Springer Science & Business Media |

Total Pages | : 192 |

Release | : 2013-12-11 |

Genre | : Mathematics |

ISBN | : 9789401764018 |

**Download The Lerch zeta function Book in PDF, Epub and Kindle**

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.

### Contributions To The Theory Of Zeta functions The Modular Relation Supremacy

Author | : Shigeru Kanemitsu,Haruo Tsukada |

Publsiher | : World Scientific |

Total Pages | : 316 |

Release | : 2014-12-15 |

Genre | : Mathematics |

ISBN | : 9789814449632 |

**Download Contributions To The Theory Of Zeta functions The Modular Relation Supremacy Book in PDF, Epub and Kindle**

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.