Abstract:Given an orthogonal polynomial sequence on the real line, another sequence of polynomials can be found by composing these polynomials with a general Möbius transformation. In this work, we study the properties of such Möbius-transformed polynomials. We show that they satisfy an orthogonality relation in given curve of the complex plane with respect to a varying weight function and that they also enjoy several properties common to the orthogonal polynomial sequences on the real line -e.g. a three-term recurrenc… Show more
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