Discriminant of the algebraic spectrum of a singular sextic oscillator factors with a squared generalized Hermite polynomial, so level crossings exactly coincide with poles of rational Painlevé IV solutions.
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Generalized Hermite Polynomials and Spectral Degeneracies of a Singular Sextic Oscillator
Discriminant of the algebraic spectrum of a singular sextic oscillator factors with a squared generalized Hermite polynomial, so level crossings exactly coincide with poles of rational Painlevé IV solutions.