The Lerch Zeta function III. Polylogarithms and special values
نویسندگان
چکیده
منابع مشابه
Special Values of Multiple Polylogarithms
Historically the polylogarithm has attracted specialists and non specialists alike with its lovely evaluations Much the same can be said for Euler sums or multiple harmonic sums which within the past decade have arisen in combinatorics knot theory and high energy physics More recently we have been forced to consider multidimensional extensions encompassing the classical polylogarithm Euler sums...
متن کاملSpecial Values of Multidimensional Polylogarithms
Historically, the polylogarithm has attracted specialists and non-specialists alike with its lovely evaluations. Much the same can be said for Euler sums (or multiple harmonic sums), which, within the past decade, have arisen in combinatorics, knot 1 theory and high-energy physics. More recently, we have been forced to consider mul-tidimensional extensions encompassing the classical polylogarit...
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It appears that the only known representations for the Riemann zeta function ζ(z) in terms of continued fractions are those for z = 2 and 3. Here we give a rapidly converging continued-fraction expansion of ζ(n) for any integer n ≥ 2. This is a special case of a more general expansion which we have derived for the polylogarithms of order n, n ≥ 1, by using the classical Stieltjes technique. Our...
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The present work is a sequel to the papers [3] and [4], and it aims at introducing and investigating a new generalized double zeta function involving the Riemann, Hurwitz, Hurwitz-Lerch and Barnes double zeta functions as particular cases. We study its properties, integral representations, differential relations, series expansion and discuss the link with known results.
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ژورنال
عنوان ژورنال: Research in the Mathematical Sciences
سال: 2016
ISSN: 2197-9847
DOI: 10.1186/s40687-015-0049-2