Some evaluation of q-analogues of Euler sums

被引：0
作者：
Ce Xu
Mingyu Zhang
Weixia Zhu
机构：
[1] Xiamen University,School of Mathematical Sciences
来源：
Monatshefte für Mathematik | 2017年 / 182卷
关键词：
q-Polylogarithm function; q-Euler sums; q-Riemann zeta function; 05A30; 65B10; 33D05; 11M99; 11M06; 11M32; 33B15;
D O I：
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学科分类号：
摘要：
In this paper, we discuss the analytic representations of q-Euler sums which involve q-harmonic numbers through q-polylogarithms, either linearly or nonlinearly, and give explicit formulae for several classes of q-Euler sums in terms of q-polylogarithms and q-special functions. Furthermore, we develop new closed form representations of sums of quadratic and cubic parametric q-Euler sums. Finally, we can find that the q-Euler sums are reducible to the classical Euler sums when q approaches 1.
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页码：957 / 975
页数：18
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