Stieltjes常数的参数化求和关系
Parameterized summation relations for the Stieltjes constants
摘要：
Stieltjes常数$γ_k(a)$出现在Hurwitz zeta函数关于其在$s=1$的唯一极奇点的Laurent展开的规则部分中。我们提出了多参数求和的关系，这些常数，导致从身份的赫维茨zeta函数。我们还提出了多参数求和关系的功能$A_k(x)$，可以表示为总和的Stieltjes常数。积分表示，特别是包括梅林变换，起着重要的作用。作为副产品，可以获得polygamma函数和伯努利多项式的互易性和其他求和关系。
英文摘要：
The Stieltjes constants $γ_k(a)$ appear in the regular part of the Laurent expansion of the Hurwitz zeta function about its only polar singularity at $s=1$. We present multi-parameter summation relations for these constants that result from identities for the Hurwitz zeta function. We also present multi-parameter summation relations for functions $A_k(x)$ that may be expressed as sums over the Stieltjes constants. Integral representations, especially including Mellin transforms, play an important role. As a byproduct, reciprocity and other summatory relations for polygamma functions and Bernoulli polynomials may be obtained.
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