论文标题
与Hurwitz的Zeta功能，Euler多项式和Euler数字有关的总和和积分家族的一些补充
Some Additions to a Family of Sums and Integrals related to Hurwitz' Zeta Function(s), Euler polynomials and Euler Numbers
论文作者
论文摘要
在半无限范围内涉及内核函数$ sech（πx）$的积分在研究Riemann函数$ζ$和Hurwitz'函数$ζ（S，A）$方面具有普遍兴趣。此类积分在此处通过$ζ（S，A）$进行评估，其中包括$ arctan $和$ log $函数，从而在此处评估，从而将一些新成员添加到已知的相关积分家族中。验证了Odd Integer参数和此类积分之间的$ζ（S）$之间的声称的连接。
Integrals involving the kernel function $sech (πx)$ over a semi-infinite range are of general interest in the study of Riemann's function $ζ(s)$ and Hurwitz' function $ζ(s,a)$. Such integrals that include the $arctan$ and $log$ functions in the integrand are evaluated here in terms of $ζ(s,a)$, thereby adding some new members to a known family of related integrals. A claimed connection between $ζ(s)$ of odd integer argument and such integrals is verified.
