A partial-sum deformation for a family of orthogonal polynomials
Abstract
There are several questions one may ask about polynomials qm(x)=qm(x;t)=Σn=0mtmpn(x) attached to a family of orthogonal polynomials \pn(x)\n0. In this note we draw attention to the naturalness of this partial-sum deformation and related beautiful structures. In particular, we investigate the location and distribution of zeros of qm(x;t) in the case of varying real parameter t.
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