کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
5775081 1413574 2017 27 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Transformation of generalized multiple Riemann zeta type sums with repeated arguments
ترجمه فارسی عنوان
تبدیل مقادیر نوع چندگانه ممتاز چندگانه ریمان زتا با استدلالات مکرر
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات آنالیز ریاضی
چکیده انگلیسی
The aim of this paper is the study of a transformation dealing with the general K-fold infinite series of the form∑n1≥⋯≥nK≥1∏j=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 ζ⋆({s}K) when an=1/ns. Our result reduces ∑∏anj 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 ζ⋆(a,b;{s}K). We construct an effective algorithm enabling the complete evaluation of ζ⋆(a,b;{2s}K) with a∈{0,−1/2}, b∈R∖{0}, (K,s)∈N2, 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 ζ⋆({2s}K) and ζ⋆({3}K) corresponding to a=b=0.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Mathematical Analysis and Applications - Volume 449, Issue 1, 1 May 2017, Pages 490-513
نویسندگان
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