On the ?-multiple Meixner polynomials of the second kind

Abstract

In this study, a new family of discrete multiple orthogonal polynomials, namely, omega-multiple Meixner polynomials of the second kind, where omega is a positive real number which is introduced. Some structural properties for these polynomials such as raising operator, Rodrigue's type formula and explicit representation are obtained. Generating function for omega-multiple Meixner polynomials of the second kind and several consequences using this generating function for these polynomials are derived. A lowering operator for omega-multiple Meixner polynomials of the second kind which will be helpful for obtaining difference equation is derived. By combining the lowering operator and the raising operator the difference equation having the omega-multiple Meixner polynomials of the second kind as a solution is obtained. A third-order explicit difference equation for omega-multiple Meixner polynomials of the second kind is given as a corollary. It is proven that when omega=1, the obtained results coincide with the existing results for multiple Meixner polynomials of the second kind. In the last section, the case when omega=5/3 is studied and for the 5/3-multiple Meixner polynomials of the second kind the explicit form, generating function and the third-order difference equation is given.