ON A REPRESENTATION OF THE RIEMANN ZETA FUNCTION

Authors

  • Ye.S. Mkrtchyan Chair of Numerical Analysis and Mathematical Modeling, YSU, Armenia

DOI:

https://doi.org/10.46991/PYSU:A/2016.50.2.035

Keywords:

Riemann function, Euler–Mascheroni constant, entire function, power series

Abstract

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.

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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