Abstract
The presented formulas and inequalities are based on interconnection of convolution and hypergeometric properties. Some known transformations and a direct coefficient technique are combined to analyze and structure a parameterized product identity involving three Gauss hypergeometric functions. A convolution presentation of this identity is a generalization of the Bateman and Kapteyn integrals for Bessel functions as well as of the addition theorem for the confluent hypergeometric functions. These results and integral properties of weighted convolutions lead to multiparameter weighted norm inequalities for generalized hypergeometric functions and special functions of hypergeometric type, in particular, for Bessel and Whittaker functions, and Laguerre and Hermite polynomials.
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