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Series Associated With the Zeta and Related Functions
Hari M. Srivastava
Junesang Choi
出版
Springer Science & Business Media
, 2001
主題
Mathematics / General
Mathematics / Calculus
Mathematics / Counting & Numeration
Mathematics / Differential Equations / General
Mathematics / Number Systems
Mathematics / Number Theory
Mathematics / Probability & Statistics / Stochastic Processes
Mathematics / Mathematical Analysis
Mathematics / Functional Analysis
Mathematics / Complex Analysis
Mathematics / Numerical Analysis
ISBN
0792370546
9780792370543
URL
http://books.google.com.hk/books?id=NBcSzUlaWWAC&hl=&source=gbs_api
EBook
SAMPLE
註釋
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.