Eur. Phys. J. D 15, 41-46 (2001)
https://doi.org/10.1007/s100530170181

Accurate summation of the perturbation series for periodic eigenvalue problems

¹ CEQUINOR (Conicet), Facultad de Ciencias Exactas, Universidad Nacional de La Plata, Calle 47 y 115, Casilla de Correo 962, 1900 La Plata, Argentina
² Departamento de Química, Facultad de Ciencias Exactas y Naturales, Universidad Nacional de Mar del Plata, Funes 3350, 7600 Mar del Plata, Argentina

Corresponding author: ^a framfer@isis.unlp.edu.ar or fernande@quimica.unlp.ar

Received: 6 December 2000
Published online: 15 July 2001

Abstract

We show that algebraic approximants prove suitable for the summation of the perturbation series for the eigenvalues of periodic problems. Appropriate algebraic approximants constructed from the perturbation series for a given eigenvalue provide information about other eigenvalues connected with the chosen one by branch points in the complex plane. Such approximants also give those branch points with remarkable accuracy. We choose Mathieu's equation as illustrative example.