Geodesic
Some infinite sums identities
Czechoslovak Mathematical Journal, Tome 65 (2015) no. 3, pp. 819-827
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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 $.
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 $.
DOI : 10.1007/s10587-015-0210-5
Classification : 11M32, 11M36
Keywords: multiple zeta values; multiple Hurwitz zeta values 
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Jaban, Meher; Bala, Sinha Sneh. Some infinite sums identities. Czechoslovak Mathematical Journal, Tome 65 (2015) no. 3, pp. 819-827. doi: 10.1007/s10587-015-0210-5

[1] Mező, I.: Some infinite sums arising from the Weierstrass product theorem. Appl. Math. Comput. 219 (2013), 9838-9846. | DOI | MR | Zbl

[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 | Zbl

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