Abstract
We consider the sum of the first two or three terms from the McMahon asymptotic expansion of the zeros of the cylinder function Cν(x) = Jν(x)cos α-Yν(x)sin α, 0⩽α<π and study when this sum represents as an upper or lower bound for the corresponding zero. The results established extend - in particular - the case of the zeros of Jν(x), when we recover the inequalities found by Förster and Petras (Förster K J and Petras K 1993 ZAMM 73 232-6) for -½⩽ν⩽½. Our approach is based on a Sturmian comparison theorem discussed in section 2.