Series Associated with the Zeta and Related Functions

Authors: Srivastava, Hari M., Junesang Choi

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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.

Buy this book

Softcover $99.00
price for USA
  • ISBN 978-90-481-5728-0
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.

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Bibliographic Information

Bibliographic Information
Book Title
Series Associated with the Zeta and Related Functions
Authors
Copyright
2001
Publisher
Springer Netherlands
Copyright Holder
Springer Science+Business Media Dordrecht
Softcover ISBN
978-90-481-5728-0
Edition Number
1
Number of Pages
IX, 388
Number of Illustrations and Tables
1 b/w illustrations
Topics