HAHN'S PROBLEM WITH RESPECT TO SOME PERTURBATIONS OF THE RAISING OPERATOR \(X-c\)

Baghdadi Aloui     (University of Gabes, Higher Institute of Industrial Systems of Gabes, Street Salah Eddine Elayoubi, 6033 Gabes, Tunisia)
Jihad Souissi     (University of Gabes, Faculty of Sciences of Gabes, Street Erriadh 6072 Gabes, Tunisia)

Abstract


In this paper, we study the Hahn's problem with respect to some raising operators perturbed of the operator \(X-c\), where \(c\) is an arbitrary complex number. More precisely, the two following characterizations hold: up to a normalization, the \(q\)-Hermite (resp. Charlier) polynomial is the only \(H_{\alpha,q}\)-classical (resp. \(\mathcal{S}_{\lambda}\)-classical) orthogonal polynomial, where \(H_{\alpha, q}:=X+\alpha H_q\) and \(\mathcal{S}_{\lambda}:=(X+1)-\lambda\tau_{-1}.\)


Keywords


Orthogonal polynomials, Linear functional, \(\mathcal{O}\)-classical polynomials, Raising operators, \(q\)-Hermite polynomials, Charlier polynomials

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References


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DOI: http://dx.doi.org/10.15826/umj.2020.2.002

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