Orthogonality via Transforms
Let e(x, t) = ∑pn (x)tn be the generating function of a polynomial sequence, and the transform of multiplication by x relative to e(x, t). We show that the sequence pn (x) is orthogonal precisely when is a t‐variable, i.e., maps K[t] into itself and increases degree by 1. We also show how transform techniques can shed light on the recursion relations and differential equations for pn (x).
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Document Type: Research Article
Affiliations: Florida Atlantic University
Publication date: October 1, 1987