Convergence acceleration of series through a variational approach

TL;DR

This paper introduces a variational method to derive new exponentially convergent series representations for mathematical constants and functions, enhancing analytical approximation techniques.

Contribution

It presents a novel variational approach that generates exponentially convergent series for constants and functions, improving upon existing series representations.

Findings

Derived new series for π and Catalan constant

Obtained series for Riemann zeta function

Method applicable to a wide class of functions

Abstract

By means of a variational approach we find new series representations both for well known mathematical constants, such as $\pi$ and the Catalan constant, and for mathematical functions, such as the Riemann zeta function. The series that we have found are all exponentially convergent and provide quite useful analytical approximations. With limited effort our method can be applied to obtain similar exponentially convergent series for a large class of mathematical functions.