Autoconvolution equations and special functions

Abstract

Autoconvolution equations of the third kind are derived for some classes of special functions as generalized Mittag–Leffler functions E α, β, error functions, and generalized Volterra functions ν, μ. These equations generalize the well-known equation by Bernstein and Doetsch for the Mittag–Leffler function E α and an equation by Janno and the author for the Volterra function ν. In addition, some autoconvolution equations of the first kind for error functions and two integro-differential equations with autoconvolution integral for the derivative of Volterra functions are given.