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arXiv · 2105.12779

The annihilation operator for certain family of q-Hermite Sobolev-type orthogonal polynomials

Carlos Hermoso·Anier Soria-Lorente
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Abstract

We present a new family $\left\{ S_{n}(x;q)\right\} _{n\geq 0}$ of monic polynomials in $x$, orthogonal with respect to a Sobolev-type inner product related to the $q$-Hermite I orthogonal polynomials, involving a first-order $q$-derivative on a mass-point $\alpha \in \mathbb{R}$ located out of the corresponding orthogonality interval $[-1,1]$, for some fixed real number $q \in (0, 1)$. We present connection formulas, and the annihilation operator for this non-standard orthogonal polynomial family.

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Carlos Hermoso, Anier Soria-Lorente. 2021-05-26. The annihilation operator for certain family of q-Hermite Sobolev-type orthogonal polynomials. https://arxiv.org/abs/2105.12779

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