On some series of special functions

Series of the form ∑k=0∞∏i=1p(ai)k∏j=1q(bj)kwkFk(z) are considered, where Fk(z) are special functions of hypergeometric type. Various types of series involving Bessel, Struve, incomplete gamma functions, and Laguerre, Hermite, Jacobi, Legendre, and Chebyshev polynomials are represented in terms of the Kampé de Fériet and generalized Horn hypergeometric functions of two variables.