Asymptotics of convergence radii for the two-parameter airy equation

Let mu(1)(lambda) < mu(2)(lambda) < mu(3)(lambda) < ... denote the eigenvalue functions of the two-parameter Airy equation y " + (mu + lambda x)y = 0, y(-1) = y(1) = 0; and let rho(n) be the radius of convergence of the expansion of mu(n)(lambda) in powers of lambda. It is shown that the sequence rho(n) satisfies the asymptotic expansion rho(n) = 9/32 pi(2)n(2) + (n(5/3)) as n --> infinity. AMS (MOS) subject classification: 33C10, 34B30.