Peter Szego

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

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

Some Monotonicity Properties of Bessel Functions

It is proved that the sequence \[\left\{ {\int_{C_\nu k}^{C_\nu ,k + 1} {t^{\gamma - 1} \left| {\mathcal{C}_\nu (t)} \right|dt} } \right\}_{k = \kappa }^\infty \] is decreasing for all

BESSEL FUNCTIONS IN A QUANTUM-BILLIARD CONFIGURATION PROBLEM

\nu

A Bessel function inequality connected with stability of least square smoothing, II

, for

Higher monotonicity properties of certain Sturm-Liouville functions

- \infty < \gamma < \frac{3}{2}

Higher monotonicity properties of certain Sturm-Liouville functions. III

, and for suitable

On the zeros of derivatives of Bessel functions

\varkappa

A singular integral whose kernel involves a Bessel function

, where

Bounds and monotonicities for the zeros of derivatives of ultraspherical Bessel functions

C_\nu (t)

Inflection points of Bessel functions of negative order

is an arbitrary Bessel function of order