Some infinite sums identities
Czechoslovak Mathematical Journal (2015)
- Volume: 65, Issue: 3, page 819-827
- ISSN: 0011-4642
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topJaban, Meher, and Bala, Sinha Sneh. "Some infinite sums identities." Czechoslovak Mathematical Journal 65.3 (2015): 819-827. <http://eudml.org/doc/271828>.
@article{Jaban2015,
abstract = {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 $.},
author = {Jaban, Meher, Bala, Sinha Sneh},
journal = {Czechoslovak Mathematical Journal},
keywords = {multiple zeta values; multiple Hurwitz zeta values},
language = {eng},
number = {3},
pages = {819-827},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Some infinite sums identities},
url = {http://eudml.org/doc/271828},
volume = {65},
year = {2015},
}
TY - JOUR
AU - Jaban, Meher
AU - Bala, Sinha Sneh
TI - Some infinite sums identities
JO - Czechoslovak Mathematical Journal
PY - 2015
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 65
IS - 3
SP - 819
EP - 827
AB - 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 $.
LA - eng
KW - multiple zeta values; multiple Hurwitz zeta values
UR - http://eudml.org/doc/271828
ER -
References
top- Mező, I., 10.1016/j.amc.2013.03.122, Appl. Math. Comput. 219 (2013), 9838-9846. (2013) Zbl1312.33060MR3049605DOI10.1016/j.amc.2013.03.122
- 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. (2006) Zbl1124.11046MR2279934
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