a1 Department of Mathematics, University of Dundee
This paper proves some inequalities for the imaginary part of the transcendental function in a simply connected sector of the complex z-plane, where 0 < v < 1, and part of the boundary depends on v. These inequalities arose in a work of Everitt and Jones  which was on a general integral inequality. We give an alternative method of proving these Bessel function inequalities.
(Received November 14 1977)
* This paper was assisted in publication by a grant from the Carnegie Trust for the Universities of Scotland.