Expansions of the Riemann Zeta function in the critical strip

TL;DR

This paper introduces new conjectural expansions of the Riemann Zeta function within the critical strip using special functions like Hermite and Laguerre, involving polynomials with zeros on the critical line.

Contribution

It proposes novel conjectural expansions of the Riemann Zeta function using special functions and polynomials with zeros on the critical line.

Findings

Formulated conjectural expansions involving special functions

Identified polynomials with zeros on the critical line

Provided a framework for further investigation of the Zeta function

Abstract

We use expansions with functions related to some special functions such as Hermite or Laguerre to get some conjectural expansions of the Riemann Zeta function in the critical strip involving a set of polynomials which have their zeros on the line Re(s)=1/2..