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multiple zeta values; multiple Hurwitz zeta values
We find the sum of series of the form $$ \sum _{i=1}^{\infty } \frac {f(i)}{i^{r}} $$ for some special functions $f$. The above series is a generalization of the Riemann zeta function. In particular, we take $f$ as some values of Hurwitz zeta functions, harmonic numbers, and combination of both. These generalize some of the results given in Mező's paper (2013). We use multiple zeta theory to prove all results. The series sums we have obtained are in terms of Bernoulli numbers and powers of $\pi $.
[1] Mező, I.: Some infinite sums arising from the Weierstrass product theorem. Appl. Math. Comput. 219 (2013), 9838-9846. DOI 10.1016/j.amc.2013.03.122 | MR 3049605 | Zbl 1312.33060
[2] Murty, M. R., Sinha, K.: Multiple Hurwitz zeta functions. Multiple Dirichlet Series, Automorphic Forms, and Analytic Number Theory. Proceedings of the Bretton Woods workshop on multiple Dirichlet series, Bretton Woods, USA, 2005. S. Friedberg et al. Proc. Sympos. Pure Math. 75 American Mathematical Society, Providence (2006), 135-156. MR 2279934 | Zbl 1124.11046
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