Formulas for special functions of mathematical physics connected with unimodular pseudoorthogonal groups

Some new formulas containing Gauss hypergeometric function, $_3F_2$-function, Meyer $G$-function, Bessel, MacDonald and Whittaker functions are obtained by group theoretical methods in this paper. The support of our approach is the most degenerated representation of unimodular pseudoorthogonal group $SO(p,q)$ into group of automorphisms of the linear space $D_\sigma$ of infinitely differentiable $\sigma$-homogeneous functions defined on a cone in $\mathbf R^{p+q}$. We considered the matrix elements of transforms of basises of $D_\sigma$ and the matrix elements of the values of above representation and its subrepresentations. The relations between these elements induced new formulas for above special functions of mathematical physics.