On the properties for modifications of classical orthogonal polynomials of discrete variables (Q1917926)

The authors study modifications of the moment functional of classical orthogonal polynomials of a discrete variable by adding a mass point at \(x=0\). In the case of the classical Meixner, Krawtchouk and Charlier polynomials they derive a representation as hypergeometric series for the corresponding modified orthogonal polynomials. They also give a second-order difference equation and a three-term recurrence relation satisfied by these modifications of the classical orthogonal polynomials. They point out the relation between the tridiagonal Jacobi matrices corresponding to the classical and to the modified orthogonal polynomials. Finally, they comment on the associated polynomials related to these modifications of the Meixner, Krawtchouk and Charlier polynomials. Some of the results for modifications of the Meixner polynomials were given before by \textit{R. Álvarez-Nodarse} and \textit{F. Marcellán} [J. Math. Anal. Appl. 194, No. 1, 250-258 (1995; Zbl 0834.39005)].