Dirichlet average and a new class of hypergeometric functions (Q2751686)

Concept of Dirichlet average, which is also called the weighted average, is a less explored branch of mathematical analysis. It denotes a certain kind of integral average with respect to a complex measure and satisfy a special class of partial differential equations and are used to evaluate certain integrals involving classical orthogonal polynomials and elliptic integrals. This excavation by the author is one such venture, where the Dirichlet average of the product \(e^{\lambda t}t^{-\tau}\) with respect to a complex measure \(\mu_b\) has been evaluated and has been expressed in terms of fractional integral operators and confluent hypergeometric functions of two variables. Main results are given in section 2, while Section 3 gives elegant results of derivatives of Dirichlet average. References are exhaustive and one may, with their aid, encounter this branch of analysis.NEWLINENEWLINEFor the entire collection see [Zbl 0970.00018].