We discuss a close connection bebveen the formula of Banks, Bender, and Wu for the asymptotics of the Rayleigh-Schrodinger coefficients of the two-dimensional rotationally symmetric anharmonic oscillator and the behavior of resonances of the hydrogen %ark problem in teo regimes: small field {Oppenheimer's formula) and large field {where we obtain the new results argg -~/ 3, I FI -o. '[&OnF) ]'I' for F, the electric field strength, going to infinity). We also Announce a rigorous proof of Bender-Wu-type formulas.
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