2019/01/28 by Artur Kawalec, Kawalec, Artur
Mathematics · #Advanced Mathematical Identities #Analytic Number Theory Research #FOS: Mathematics #General Mathematics (math.GM) #Meromorphic and Entire Functions
paper · pdf · doi:10.48550/arxiv.1901.09519
openalex publication_date 2019/01/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this article, we derive a Euler prime product formula for the magnitude of the Riemann zeta function ζ(s) valid for \Re(s)>1, as well as similar formulas for ζ(s) valid for an even and odd kth positive integer argument. We shall further give a set of generated formulas for ζ(k) up to 11th order, including Apéry's constant, and also construct formulas for ζ(3/2). We'll also validate these formulas numerically.