Pseudo-Poles in the Theory of Emden's Equation

Abstract

It is known that Emden's equation y'' = x(1-m)y(m) has movable singularities where the solution becomes infinite for one-sided approach. If m = (p + 2)/p, p positive integer, the singularities look like poles of order p. In this note expansions in terms of powers and logarithms are obtained from which the nonpolar nature of these "pseudo-poles" becomes evident. Various extensions are considered. Convergence proofs are deferred to a more detailed publication.