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 Forster and Petras (Forster 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.
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