Representation of Weierstrass integral via Poisson integrals

In our research, we have presented a second-order linear partial differential equation in polar coordinates. Considering this on the unit disk, obtained one-dimensional heat equation. It is well-known that can be solved taking into account boundary condition for general solution circle. paper, boundary-value problem using method called separation of variables. As result, to terms Fourier series. Then expressions coefficients are used transform series expansion so-called Weierstrass integral, which represented via kernel. A representation kernel infinite geometric derived by way allowing complicated function parameterized simplified function. The derivation corresponding parametrization based two integrals. natural argument form double integral contains same argument. So, double-integral has been derived. To obtain Dirac delta taken account. expression found substituted integral. it was considered Poisson and conjugate