The p-adic Arakawa–Kaneko–Hamahata zeta functions and poly-Euler polynomials
The p-adic Arakawa–Kaneko–Hamahata zeta functions and poly-Euler polynomials
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DOI：
10.1016/j.jnt.2017.01.017
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发表时间：
2017-08
影响因子：
0.7
通讯作者：
Su Hu;Dae-Jung Kim;Min-Soo Kim
中科院分区：
文献类型：
--
作者：
Su Hu;Dae-Jung Kim;Min-Soo Kim
本文给出了p进Arakawa-Kaneko-Hamahata zeta函数的定义。这些zeta函数在非正整数处插值Hamahata的多欧拉多项式。我们证明了这些zeta函数的导数公式、差分方程和反射公式。此外，我们还证明了Hamahata多项式的乘积和恒等式和关于第二类斯特林数的一个封闭形式。
In this paper, we give a definition of thep-adic Arakawa–Kaneko–Hamahata zeta functions. These zeta functions interpolate Hamahata's poly-Euler polynomials at non-positive integers. We prove the derivative formula, the difference equation and the reflection formula of these zeta functions. Furthermore, we also prove a sums of products identity and a closed form of Hamahata's poly-Euler polynomials in terms of the Stirling numbers of the second kind.