A generalization of a theorem of Nehari

Abstract

In 1956 Nehari, [N.l] showed that the singular points to of the Legendre series, (i) *(o = <*nP(o, |* + i| + h-i|<p +-* n-*0 P where lirn sup^*, | a n \ lln -p-1 < 1, are related to the singular points f o of the associated power series, (2) /(f) = E^r, k | <P~S by the formula Jo = 10*0 + 1/To), providing UT\. The purpose of this note is to announce similar results concerning the singularities of functions <j>(z) defined by series of the form ^"o <Wn(s), where the v n (z) are normalized eigenfunctions of the Sturm-Liouville system *"(*) + (P 2 -M) = o, z/(0) + Av(0) = !>' (TT) + BV(T) = 0.