Logo - springer
Slogan - springer

Mathematics - Number Theory and Discrete Mathematics | Series Associated with the Zeta and Related Functions

Series Associated with the Zeta and Related Functions

Srivastava, Hari M., Junesang Choi

Softcover reprint of the original 1st ed. 2001, IX, 388 p.

Softcover
Information

Softcover (also known as softback) version.

You can pay for Springer Books with Visa, Mastercard, American Express or Paypal.

Standard shipping is free of charge for individual customers.

(net) price for USA

ISBN 978-90-481-5728-0

free shipping for individuals worldwide

usually dispatched within 3 to 5 business days


add to marked items

$99.00
  • About this book

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.

Content Level » Research

Related subjects » Analysis - Computational Science & Engineering - Number Theory and Discrete Mathematics

Table of contents 

Preface. Acknowledgements. 1. Introduction and Preliminaries. 2. The Zeta and Related Functions. 3. Series Involving Zeta Functions. 4. Evaluations and Series Representations. 5. Determinants of the Laplacians. 6. Miscellaneous Results. Bibliography. Author Index. Subject Index.

Popular Content within this publication 

 

Articles

Services for this book

New Book Alert

Get alerted on new Springer publications in the subject area of Number Theory.