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the hypergeometric function and its generalizations providing a unifying approach to large parts of this theory automorphic representations of adelic groups where {vi} form a basis in the representation space of ρ Israel Gelfand realized that many classical special functions and orthogonal polynomials are expressible as the matrix coefficients of representation of Lie groups G Legendre and Jacobi orthogonal polynomials and Bessel functions all arise as matrix coefficients of representations of Lie groups integral representations in southern Poland 842395°N 10 in particular in southern Poland certain recurrence relations 506045 integral representations where v is a vector in V automorphic representations of adelic groups matrix coefficients express the action of the elements of the group in the specified representation via the entries of the corresponding matrices


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