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A Probabilistic Proof for Representations of the Riemann Zeta Function

School of Statistics, Qufu Normal University, Shandong 273165, China
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Mathematics 2019, 7(4), 369; https://doi.org/10.3390/math7040369
Received: 4 April 2019 / Revised: 18 April 2019 / Accepted: 19 April 2019 / Published: 24 April 2019
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Abstract

In this paper, we present a different proof of the well known recurrence formula for the Riemann zeta function at positive even integers, the integral representations of the Riemann zeta function at positive integers and at fractional points by means of a probabilistic approach. View Full-Text
Keywords: Bernoulli numbers; (half-) logistic distribution; integral representation; probabilistic approach; Riemann zeta function Bernoulli numbers; (half-) logistic distribution; integral representation; probabilistic approach; Riemann zeta function
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
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Liu, J.; Huang, Y.; Yin, C. A Probabilistic Proof for Representations of the Riemann Zeta Function. Mathematics 2019, 7, 369.

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