Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5775081 | Journal of Mathematical Analysis and Applications | 2017 | 27 Pages |
Abstract
The aim of this paper is the study of a transformation dealing with the general K-fold infinite series of the formân1â¥â¯â¥nKâ¥1âj=1Kanj, especially those, where an=R(n) is a rational function satisfying certain simple conditions. These sums represent the direct generalization of the well-known multiple Riemann zeta-star function with repeated arguments ζâ({s}K) when an=1/ns. Our result reduces ââanj to a special kind of one-fold infinite series. We apply the main theorem to the rational function R(n)=1/((n+a)s+bs) in case of which the resulting K-fold sum is called the generalized multiple Hurwitz zeta-star function ζâ(a,b;{s}K). We construct an effective algorithm enabling the complete evaluation of ζâ(a,b;{2s}K) with aâ{0,â1/2}, bâRâ{0}, (K,s)âN2, by means of a differential operator and present a simple 'Mathematica' code that allows their symbolic calculation. We also provide a new transformation of the ordinary multiple Riemann zeta-star values ζâ({2s}K) and ζâ({3}K) corresponding to a=b=0.
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Marian GenÄev,