Ovcharenko O. New generalizations of hypergeometric type functions and their applications

The thesis deals with studying of new generalized functions of hypergeometric type. Their main properties and applications to integral equations, differential equations, integral transforms are given. New generalized functions of hypergeometric type, generalized gamma and beta-functions are introduced. For these functions a number of recurrent functional, differential and integral relations are proved. Their applications in the theory of integral equations, fractional integration and differentiation theory, probability theory are considered. For new generalized hypergeometric function the asymptotic expansions are obtained.