Summary
A form (linear functional) $u$ is called regular if we can associate with it a sequence of monic orthogonal polynomials. On certain regularity conditions, the product of a non regular form by a polynomial can be regular. The purpose of this work is to establish regularity conditions of the form $-(x-c){\mathbf S}',$ where ${\mathbf S}$ is a classical (Bessel, Jacobi). We give the second-order recurrence relations and structure relations of its corresponding orthogonal polynomial sequence. We conclude with an example as an illustration.
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Sfaxi, R., Alaya, J. On orthogonal polynomials with respect to the form -(x - c)S'. Period Math Hung 52, 67–99 (2006). https://doi.org/10.1007/s10998-006-0006-3
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DOI: https://doi.org/10.1007/s10998-006-0006-3