Über eine partielle Differentialgleichung mit p+2 Variablen und deren Zusammenhang mit den allgemeinen Kugelfunktionen

This paper essentially deals with operators that map harmonic functions into solutions of a class of elliptic partial differential equations in p+2 variables. Starting with the representation by means of integral operators, obtained by R. P. Gilbert, a representation free of integrals is derived by using the properties of the Riemann function. This operator has a very simple form-there are only used differential operators with respect to a parameter. Furthermore,with this result, we are able to give a representation formula for the Spherical Harmonics of degree N in 2l+1 dimensions, similar to that given by K. W. Bauer.