Sobolev orthogonal polynomials: Connection formulae

Abstract

This contribution aims to obtain several connection formulae for the polynomial sequence, which is orthogonal with respect to the discrete Sobolev inner product \[ \langle f, g\rangle_n=\langle {\bf u}, fg\rangle+ \sum_{j=1}^M \mu_{j} f^{(\nu_j)}(c_j) g^{(\nu_j)}(c_j), \] where \({\bf u}\) is a classical linear functional, \(c_j\in \mathbb R\), \(\nu_j\in \mathbb N_0\), \(j=1, 2,...., M\). The Laguerre case will be considered.

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@article{costas2022sobolev,
TITLE={Sobolev orthogonal polynomials: Connection formulae},
AUTHOR={Costas-Santos, R. S.},
JOURNAL={Redel. Revista Granmense de Desarrollo Local},
VOLUME={6},
NUMBER={4},
PAGES={25--34},
YEAR={2022},
URL={https://ediciones.udg.co.cu/libros/index.php/libros/catalog/view/26/56/135-1},
}