ON A REPRESENTATION OF THE RIEMANN ZETA FUNCTION
DOI:
https://doi.org/10.46991/PYSU:A/2016.50.2.035Keywords:
Riemann function, Euler–Mascheroni constant, entire function, power seriesAbstract
In this paper a new representation of the Riemann function in the disc $U(2,1)$ is obtained:$\zeta (z) = \dfrac{1}{z-1} + \displaystyle\sum_{n=0}^\infty(-1)^n\alpha_n(z-2)^n,$ where the coefficients $\alpha_k$ are real numbers tending to zero. Hence is obtained $\gamma=\displaystyle\lim_{m\rightarrow\infty}\left[\displaystyle\sum_{k=0}^n\dfrac{\zeta^{(k)}(2)}{k!}-n\right],$ where $\gamma$ is the Euler-Mascheroni constant.
Downloads
Published
2016-06-06
How to Cite
Mkrtchyan, Y. (2016). ON A REPRESENTATION OF THE RIEMANN ZETA FUNCTION. Proceedings of the YSU A: Physical and Mathematical Sciences, 50(2 (240), 35–38. https://doi.org/10.46991/PYSU:A/2016.50.2.035
Issue
Section
Mathematics
License
Copyright (c) 2016 Proceedings of the YSU
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.