Verified Computation of Lame Functions with High Accuracy

摘要

The Lame functions are of considerable interest for boundary-value problem sin electormagnetics and mechanics that involve ellipsoid geometry. Up to now efficient algorithms for the verified computation of these functions do not exist. In this article we provide a new effective scheme for the numerical treatment of Lame functions of the first and second kind. It involves computing the Lame functions with high accuracy combined with safe error estimates.