Systematic perturbation calculation of integrals with applications to physics

TL;DR

This paper enhances a method for calculating classical oscillator periods and physical integrals, providing more accurate analytical expressions and analyzing their convergence, with applications in physics.

Contribution

The authors generalize and improve a recent method for integral calculation, yielding more precise analytical formulas and assessing their convergence properties.

Findings

More accurate analytical expressions for oscillator periods.

Improved convergence of the series solutions.

Enhanced applicability to physical integrals.

Abstract

In this paper we generalize and improve a method for calculating the period of a classical oscillator and other integrals of physical interest, which was recently developed by some of the authors. We derive analytical expressions that prove to be more accurate than those commonly found in the literature, and test the convergence of the series produced by the approach.