Logarithmic functions are eigenfunctions of integral operators with M-Wright kernels

In this paper, using the Buschman's theorem for the Laplace transform, we show that the logarithmic functions phi(n)(s) = 1/s Sigma(n)(i=0)(-1)(i) [GRAPHICS] Gamma((n-i))(1) ln(i)(s), n is an element of N, are the eigenfunctions of integral operators with M-Wright kernels. Some identities are also given for connections of the Mittag-Leffler functions and phi(n)(s). (c) 2021 Elsevier B.V. All rights reserved.

Automated summary

In this paper, it is demonstrated that certain logarithmic functions are eigenfunctions of integral operators with M-Wright kernels using Buschman's theorem for the Laplace transform. Connections between Mittag-Leffler functions and these logarithmic functions are also established through various identities.