# On spectral polynomials of the Heun equation. I

@article{Shapiro2010OnSP, title={On spectral polynomials of the Heun equation. I}, author={Boris Z. Shapiro and Milos Tater}, journal={J. Approx. Theory}, year={2010}, volume={162}, pages={766-781} }

The classical Heun equation has the form {Q(z)d^2dz^2+P(z)ddz+V(z)}S(z)=0, where Q(z) is a cubic complex polynomial, P(z) is a polynomial of degree at most 2 and V(z) is at most linear. In the second half of the nineteenth century E. Heine and T. Stieltjes initiated the study of the set of all V(z) for which the above equation has a polynomial solution S(z) of a given degree n. The main goal of the present paper is to study the union of the roots of the latter set of V(z)'s when n->~. We… CONTINUE READING

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