Recursion Relations and Functional Equations for the Riemann Zeta Function

TL;DR

This paper introduces new recursion relations and functional equations for the Riemann zeta function, derived from the standard functional equation, applicable across the entire complex plane, and simplifies the relations by eliminating coefficient functions.

Contribution

It presents novel recursion relations and functional equations for the Riemann zeta function, expanding the tools available for its analysis.

Findings

Derived recursion relations from the functional equation

Functional equations applicable over the entire complex plane

Simplified relations by eliminating coefficient functions

Abstract

New recursion relations for the Riemann zeta function are introduced. Their derivation started from the standard functional equation. The new functional equations have both real and imaginary increment versions and can be applied over the whole complex plane. We have developed various versions of the recursion relations eliminating each of the coefficient functions, leaving plain zeta functions