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.
Similar content being viewed by others
Author information
Authors and Affiliations
Additional information
Received 6 December 2000
Rights and permissions
About this article
Cite this article
Fernández, F., Diaz, C. Accurate summation of the perturbation series for periodic eigenvalue problems. Eur. Phys. J. D 15, 41–46 (2001). https://doi.org/10.1007/s100530170181
Issue Date:
DOI: https://doi.org/10.1007/s100530170181