Abstract—The polynomials are applied in many areas of mathematics, for instance, continued fractions, operator theory, analytic functions, interpolation, approximation theory, numerical analysis, electrostatics, statistical quantum mechanics, special functions, number theory, combinatorics, stochastic processes. On the other hand, generating functions have a great importance in special functions theory. The present study deals with some new properties of the Meixner polynomials in several variables. Firstly, we obtained some results include various families of multilinear and multilateral generating functions for the Meixner polynomials in several variables. In the last section, we get a theorem that gives a bilateral generating functions for these polynomials and the Lauricella functions. Finally, we derive some corollaries of the last theorem.

Index Terms—Bilinear and bilateral generating function, Lauricella function, Meixner polynomials.

Nejla Özmen is with Düzce University, Faculty of Art and Science, Department of Mathematics, Konuralp TR-81620, Düzce, Turkey (email: nejlaozmen06@gmail.com).
Esra Erkus-Duman is with Gazi University, Faculty of Science, Department of Mathematics, Teknikokullar TR-06500, Ankara, Turkey.

Cite: Nejla Özmen, Esra Erkus-Duman, "The Meixner Polynomials in Several Variables," International Journal of Applied Physics and Mathematics vol. 9, no. 3, pp. 144-151, 2019.