Discrete semi-classical orthogonal polynomials: generalized Meixner
The property of quasiorthogonality of the derivative of semi classical orthogonal is extended to the discrete case for the generalized Meixner polynomials. The positive weigth \(\rho\) (x) is solution of the difference equation A(x) \(\rho\) (x\(+1)-B(x) \rho (x)=0\) with A(x) and B(x) polynomials of degree respectively \(\alpha\) and \(\beta\). The situation examined here in (0,\(\infty)\) gives the semi-Meixner case (generalized Meixner) for \(\alpha =\beta\) and would give semi-Charlier when \(\alpha >\beta\). From elementary property of the \(\Gamma\) function it could also be shown that no possibilities exist in \((-\infty,+\infty)\).
scientific article; zbMATH DE number 3948953