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Bounds for the distancejc;s c1;s0j between adjacent zeros of cylinder functions are given; s and s0 are such that @c;s00 2 )c;s;c1;s0 (; c;k stands for the kth positive zero of the cylinder (Bessel) functionC (x )= cosJ(x) sinY (x), 2 (0;(, 2R. These bounds, together with the application of modied (global) New- ton methods based on the monotonic functions f (x )= x2 1C (x)=C 1(x) and g (x )= x (2+1)C (x)=C+1(x), give rise to forward (c;k ! c;k+1) and backward (c;k+1! c;k) iterative relations between consecutive zeros of cylinder functions. The problem of nding all the positive real zeros of Bessel functionsC (x) for any real and inside an interval (x1;x2), x1 > 0, is solved in a simple way.

Bounds on differences of adjacent zeros of Bessel functions and iterative relations between consecutive zeros