Special functions related to various types of root systems

This paper describes methods that allow one to obtain special functions and study their properties. Using the differential-difference operator theory developed by Ch. Dunkl, the author constructs the family of functions associated with the root system of type G ₂. It is shown that it contains the subset consisting of the well-known Gegenbauer polynomials. Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 54, Suzdal Conference–2006, Part 2, 2008.