The relation between the 2 - monogenic funetions and the Solutions of the elliptic partial differential equation 8^U dU dx^ is known [6] ; the ohject of this paper is to investigate the properties of the generalized TricomVs Equation (*) 8Xj and its Solutions which will be composed of three sections. called as S - harmonic fujıctions. Our study is İn section I we have investigated some properties of the Solutions of the + k + — y = o n + 8 U = Q equation (*). In section II the well - known Lord Kelvin’s theorem and Almansi’s expan- sion theorem have been established for S-harmonic and S-polyharmonic funetions. In section III we have proved Brill’s theorem for S - polyharmonic funetions which was previously given for the harmonic funetions.