Abstract
Stieltjes and Van Vleck polynomials arise in the study of the polynomial solutions of the generalized Lame's differential equations. In this paper, the location of the zeros of these polynomials, relative to a prescribed location of the complex constants occurring in the differential equation is determined. Various results to this effect have been put forward from time to time by Marden, Stieltjes, Van Vleck, Bôcher, Klein, and Pólya, but all (except the one due to Marden) were obtained under very restrictive conditions on these constants. Some of these results are shown to be corollaries of our main theorem here. Moreover, applications to certain problems arising in physics and fluid mechanics are discussed.
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