Papers › A partial-sum deformation for a family of orthogonal polynomials
A partial-sum deformation for a family of orthogonal polynomials
Erik Koelink, Pablo Román, Wadim Zudilin
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There are several questions one may ask about polynomials qₘ(x)=qₘ(x;t)=∑ₙ₌₀ᵐtᵐpₙ(x) attached to a family of orthogonal polynomials {pₙ(x)}_(n≥0). 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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