A Probabilistic Proof for Representations of the Riemann Zeta Function

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.

Keywords

• Bernoulli numbers
• (half-) logistic distribution
• integral representation
• probabilistic approach
• Riemann zeta function