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Polynomial sequences associated with the classical linear functionals

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Abstract

This work in mainly devoted to the study of polynomial sequences, not necessarily orthogonal, defined by integral powers of certain first order differential operators in deep connection to the classical polynomials of Hermite, Laguerre, Bessel and Jacobi. This connection is streamed from the canonical element of their dual sequences. Meanwhile new Rodrigues-type formulas for the Hermite and Bessel polynomials are achieved.

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Correspondence to Ana Filipa Loureiro.

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Work of AFL supported by Fundação para a Ciência e Tecnologia via the grant SFRH/BPD/63114/2009. This research is partially funded by the European Regional Development Fund through the programme COMPETE and by the Portuguese government through the FCT (Fundação para a Ciência e a Tecnologia) under the project PEst-C/MAT/UI0144/2011.

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Loureiro, A.F., Maroni, P. Polynomial sequences associated with the classical linear functionals. Numer Algor 60, 297–314 (2012). https://doi.org/10.1007/s11075-012-9573-y

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