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arXiv · 2310.12312

Sobolev orthogonal polynomials: Connection formulae

Roberto S. Costas-Santos
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Abstract

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

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Roberto S. Costas-Santos. 2023-10-18. Sobolev orthogonal polynomials: Connection formulae. https://arxiv.org/abs/2310.12312

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