FORMULATION OF THE INTEGRAL FORM FOR INTEGRAL FUNCTION APPROXIMATIONS

The formulation of the problem of obtaining a unique integral form for the integral function approximation to a real-valued, locally analytic function is given. A careful distinction is made between the approximation of the integral form which defines the polynomial coefficients of the differential equation which defines the integral function, and the approximation by the integral function itself. This distinction leads to a clear treatment of the effects of degenerate cases arising from the separate steps. This paper considers the formulation of a unique integral form and a companion paper will consider the degeneracies of the integral form.