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1. Introduction. Throughout this note, cvm and yVk denote, respectively , the mth and &th positive zeros of any pair (distinct or not) of real Bessel (cylinder)3 functions of order v, arranged so that c»m>yvk, where m and k (the respective ranks) are fixed positive integers. Each such zero increases with v [6, p. 508], In particular, we may take the Bessel functions involved to be identical and put m — k+l, where / is any positive integer. When 1=1, this specializes to the familiar differences which are defined in the usual way as

Monotonicity of the differences of zeros of Bessel functions as a function of order