Representation of Dirichlet Average of K-Series via Fractional Integrals And Special Functions

The aim of this paper is to investigate the Dirichlet averages of the K- series. Representations for such constructions in two and multi-dimensional cases are derived in term of the Riemann-Liouville fractional integrals and of the hypergeometric functions of several variables. Special cases when the above Dirichlet averages coincide with different type of the Mittag-Leffler functions and hypergeometric functions of one and several variables are obtained.