BesselK Series for the Riemann Zeta function

TL;DR

This paper introduces series expansions of the Riemann xi function using Bessel K functions, offering new mathematical representations that could aid in understanding the properties of the Riemann zeta function.

Contribution

It presents novel series expansions of the Riemann xi function in terms of Bessel K functions, expanding the analytical tools available for studying the zeta function.

Findings

Derived new series representations of ξ using Bessel K functions

Potential implications for analyzing zeros of the Riemann zeta function

Provides mathematical formulas for further theoretical exploration

Abstract

This paper provides some expansions of Riemann xi function, $\xi$, as a series of Bessel K functions.