О некоторых специальных полиномах и функциях

A full system of homogeneous harmonic polynomials on $n$ variables is constructed. It is orthogonal in two spaces. On the base of these polynomials a notion of $G$-functions is introduced. Connections of $G$-functions with Legendre polynomials and Chebyshev polynomials are obtained and a Rodrigues formula is proved.