An addendum to the general coefficient theorem

Abstract

1. In our ultimate form of the General Coefficient Theorem [1, Theorem 1] we imposed a normalization on the expression for the quadratic differential at a pole of order greater than two. The purpose of this was to avoid complication in the calculations given in [1, pp. 393-394]. It was observed that thisnormalization could always be attained by a suitable change in the local parameter employed at the pole in question [1, Remark, p. 389]. The object of the present paper is to show that using the form of the General Coefficient Theorem obtained there we can without essential difficulty obtain the appropriate formulation when we drop the normalization in question. We will use throughout the notation of [1].