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Series Associated with the Zeta and Related Functions

  • Book
  • © 2001

Overview

Authors:
  1. Hari M. Srivastava

    1. Department of Mathematics & Statistics, University of Victoria, Victoria, Canada

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    You can also search for this author in PubMed   Google Scholar

  2. Junesang Choi
    View author publications

    You can also search for this author in PubMed   Google Scholar

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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.

Authors and Affiliations

  • Department of Mathematics & Statistics, University of Victoria, Victoria, Canada

    Hari M. Srivastava

Bibliographic Information

  • Book Title: Series Associated with the Zeta and Related Functions

  • Authors: Hari M. Srivastava, Junesang Choi

  • Publisher: Springer Dordrecht

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Science+Business Media Dordrecht 2001

  • Softcover ISBN: 978-90-481-5728-0Published: 02 January 2013

  • Edition Number: 1

  • Number of Pages: IX, 388

  • Number of Illustrations: 1 b/w illustrations

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