QUADRATIC GROWTH OF CONVERGENCE RADII FOR EIGENVALUES OF 2-PARAMETER STURM-LIOUVILLE EQUATIONS

The nth eigenvalue mu of the equation y '' + (mu + lambda r(x)) y = 0, a less than or equal to x less than or equal to b, subject to self-ad joint boundary conditions admits a power series expansion into powers of lambda, for sufficiently small \lambda\. It is proved that the conv ergence radii of these series grow like n(2) as n tends to infinity pr ovided r(x) is analytic on [a, b]. Applications to the Airy and Mathie u equation are given. (C) 1996 Academic Press, Inc.