Geodesic
On a representation of the Riemann zeta function
Proceedings of the Yerevan State University. Physical and mathematical sciences, no. 2 (2016), pp. 35-38

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In this paper a new representation of the Riemann zeta 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 $\gamma=\displaystyle\lim_{m\rightarrow\infty} \left[\displaystyle\sum_{k=0}^{n-1} \dfrac{\zeta^{(k)}(2)}{k!}-n\right]$, where $\gamma$ is the Euler–Mascheroni constant.
Keywords: Riemann function, entire function, power series.
Mots-clés : Euler–Mascheroni constant 
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Yе. S. Mkrtchyan. On a representation of the Riemann zeta function. Proceedings of the Yerevan State University. Physical and mathematical sciences, no. 2 (2016), pp. 35-38. http://geodesic.mathdoc.fr/item/UZERU_2016_2_a5/