Multiple power series representations for riemann functions of self-adjoint equations

Abstract

For the class of self-adjoint equations , the complex Riemann function R(z, ζ, t, τ) is explicitly given as a fivefold (resp. sixfold) infinite series in terms of four auxiliary variables which are rational functions of the variables z, ζ, t, τ, but do not depend on the parameters. The solution of two further equations are derived from this Riemann function by a linear transformation of the independent variables. For particular values of the parameters, the representation is shown to be consistent with known results.