Taylor Series of Biharmonic Poisson Integral for Upper Half-Plane

Abstract

The fourth-order partial differential equation for the biharmonic Poisson integral is presented in the case of the upper half-plane (y > 0). To solve this equation, two boundary conditions must be taken into account. The boundary-value problem is solved by transforming the presented boundary-value problem for the biharmonic Poisson integral into two boundary-value problems for some two-dimensional functions A(q, y) and B (q, y). After that, the biharmonic Poisson integral for the upper half-plane is obtained. It was found that the derived Taylor series of biharmonic Poisson integral for the upper half-plane contains the remainder in the integral form.