Page:BatemanConformal.djvu/12

1908.] The differential equation thus reduces to

This is Papperitz's form of the differential equation satisfied by Riemann's general hypergeometric function

hence we have the result that

is a homogeneous function of (l, m, n, λ, μ, ν) of degree -1, satisfying the equation

When expressed in terms of x, y, z and w, it will thus be a solution of the equation

The various transformations of the general hypergeometric function are easily obtained from this result. If we write U in the form