Matrix Gegenbauer Polynomials: the $2\times 2$ Fundamental Cases

Inés Pacharoni; Ignacio Zurrián

doi:10.1007/s00365-015-9301-7

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arXiv · 1309.6902

Matrix Gegenbauer Polynomials: the $2\times 2$ Fundamental Cases

Inés Pacharoni·Ignacio Zurrián

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Abstract

In this paper, we exhibit explicitly a sequence of $2\times2$ matrix valued orthogonal polynomials with respect to a weight $W_{p,n}$, for any pair of real numbers $p$ and $n$ such that $0<p<n$. The entries of these polynomiales are expressed in terms of the Gegenbauer polynomials $C_k^\lambda$. Also the corresponding three-term recursion relations are given and we make some studies of the algebra of differential operators associated with the weight $W_{p,n}$.

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BibTeX RIS

Inés Pacharoni, Ignacio Zurrián. 2013-09-24. Matrix Gegenbauer Polynomials: the $2\times 2$ Fundamental Cases. https://doi.org/10.1007/s00365-015-9301-7

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