Abstract
Using a particular way of normalizing the orthogonal polynomials, which is most commonly encountered in the synthesis of filtering networks in communication and electronic engineering, two theorems concerning the extremal properties of orthogonal polynomials are first proved. The results are then applied to find the minimum value and the minimizing function for various definite integrals involving weight functions of classical orthogonal polynomials.
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Rakovich, B.D., Vasić, P.M. Some extremal properties of orthogonal polynomials. Aeq. Math. 26, 125–137 (1983). https://doi.org/10.1007/BF02189677
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DOI: https://doi.org/10.1007/BF02189677