New rapidly converging series representations for values of the Riemann zeta function and the Dirichlet beta function

TL;DR

This paper introduces new rapidly converging series representations for special constants related to the Riemann zeta and Dirichlet beta functions, enhancing computational efficiency and generalizability.

Contribution

The authors derive novel series for Catalan's and Apéry's constants, with a method that can be extended to other values of the zeta and beta functions.

Findings

Derived rapidly converging series for Catalan's and Apéry's constants.

Method can be generalized to other zeta and beta function values.

Improves computational efficiency for these constants.

Abstract

In this paper we derive rapidly converging series for Catalan's constant and for Ap\'ery's constant. The method may be easily generalised to produce new series representations for other values of the Riemann zeta function and the Dirichlet beta function.