Generalized Rodriques formula solutions for certain linear differential equations
James M. Horner · Transactions of the American Mathematical Society · 1965
It was found that, when this equation has a positive integer root n, (1) has solutions which can be expressed in terms of a generalized Rodrigues formula having n 1 for the index of differentiation. For nonpositive integer roots of (2) a general solution for (1) can be given by an iterated indefinite integral and for nonintegral roots the corresponding solution is a contour integral which reduces to the Rodrigues formula for integer roots. The contour integral result was obtained only for the homogeneous form of (1). The purpose of this paper is to present the remaining results obtained by the author in [3], namely the extension of the above results for secondorder equations to certain nth-order linear differential equations. The equation to be discussed is