ON SOME QUADRATURES IN CERTAIN SPECIAL CLASSES OF THE VEKUA EQUATIONS

Abstract

In the paper, two equations with constant coefficients (1) and (17) are being considered with the method of areolar series. The solutions found are cases where an arbitrary analytic functions \(\phi=\phi(z)\) plays the role of an integrated constant. So, we get quadratures formulas for the equations of that kind. Notice that the equations (1) and (17) are special cases of the known Vekua equation, that help us to define different classes of generalised analytic functions studied by Vekua in the sense of iteration [1].