A tri-harmonic Neumann function for the unit disc

摘要

In this paper we consider a tri-harmonic Neumann function for the unit disc. The Neumann problem is well studied for harmonic functions and solved under certain conditions via the Neumann functions, sometimes also called Green function of second kind. The tri-harmonic Neumann function is constructed in an explicit way for the unit disc of the complex plane by convoluting the harmonic function with a bi-harmonic Neumann function. With this Neumann function an integral representation formula is developed for the tri-harmonic operator.