Large-Order Perturbation Theory in the Stark-Zeeman Effect for Parallel Fields

For the ground-state hydrogen atom in parallel electric and magnetic fields the coefficients in the double perturbation series are calculated to large order and certain asymptotic recurrences are stated. With use of only the real coefficients, the complex energy eigenvalue is obtained as a function of both field strengths by rational approximant methods. This represents the first application of two-variable approximants to the calculation of eigenvalues for a physical system.