La relation entre ζ(4n-1), ζ(2p) et ζ(4n-1-2p)

2024/03/26 by Kabongo, Mundankulu
#FOS: Mathematics #General Mathematics (math.GM)

paper · doi:10.48550/arxiv.2403.17997

Abstract

The functional relation of the Riemann zêta function provides us with neither the nature nor the expression of zêta at positive odd numbers. From the function F(z)=\fracz^-2ne^z-1, we find a functional relation involving ζ(4n- 1), ζ(2p) and ζ(4n-1-2p). It is given by: ζ(4n-1)=(1)/(2n-1)∑_p=1^2n-2ζ(2p)ζ(4n-1-2p). n=2, 3, 4, 5, 6, ... From this formula we introduce a new approach to study the nature of ζ on these integers.

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