کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
8899413 | 1631544 | 2018 | 17 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Some evaluation of cubic Euler sums
ترجمه فارسی عنوان
برخی از ارزیابی مبالغ مکعبی اویلر
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
آنالیز ریاضی
چکیده انگلیسی
P. Flajolet and B. Salvy [15] prove the famous theorem that a nonlinear Euler sum Si1i2â¯ir,q reduces to a combination of sums of lower orders whenever the weight i1+i2+â¯+ir+q and the order r are of the same parity. In this article, we develop an approach to evaluate the cubic sums S12m,p and S1l1l2,l3. By using the approach, we establish some relations involving cubic, quadratic and linear Euler sums. Specially, we prove the cubic sums S12m,m and S1(2l+1)2,2l+1 are reducible to zeta values, quadratic and linear sums. Moreover, we prove that the two combined sums involving multiple zeta values of depth fourâ{i,j}â{1,2},iâ jζ(mi,mj,1,1)andâ{i,j,k}â{1,2,3},iâ jâ kζ(mi,mj,mk,1) can be expressed in terms of multiple zeta values of depth â¤3, here 2â¤m1,m2,m3âN. Finally, we evaluate the alternating cubic Euler sums S1¯3,2r+1 and show that it are reducible to alternating quadratic and linear Euler sums. The approach is based on Tornheim type series computations.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Mathematical Analysis and Applications - Volume 466, Issue 1, 1 October 2018, Pages 789-805
Journal: Journal of Mathematical Analysis and Applications - Volume 466, Issue 1, 1 October 2018, Pages 789-805
نویسندگان
Ce Xu,