Quasi-exactly solvable quartic: elementary integrals and asymptotics
  We study elementary eigenfunctions y=p exp(h) of operators L(y)=y"+Py, where p, h and P are polynomials in one variable. For the case when h is an odd cubic polynomial, we found an interesting identity which is used to describe the spectral locus. We also establish some asymptotic properties of the QES spectral locus. 
Alexandre Eremenko and Andrei Gabrielov
math-ph math.CA math.MP