e-mail: Laforgia@matrm3.mat.uniroma3.it

**Inequalities and Approximations for the Zeros of Bessel
Functions**

**Abstract**

We present some results obtained in the last years on the zeros $c_{\nu,k}$
of the general Bessel function

$$C_{\nu}(x)=\cos {\alpha} \, J_\nu (x) - \sin {\alpha} Y_\nu (x),
\qquad 0 \le \alpha <\pi, $$ where $J_\nu$ and $Y_\nu$ are the
Bessel functions of the first and second kind, respectively. In particular
we discuss inequalities for a) fixed $\nu$ and large $k$; b) fixed $k$
and large $\nu$. In some cases a numerical comparison with old results
is also made.

**References**

1. Elbert A. and A. Laforgia, *An upper bound for the zeros of cylider
functions*, MIA, Mathematical Inequalities and Applications, **1**
(1998), 105-111.

2. Elbert A. and A. Laforgia, *Further results on McMahon asymptotic
approximations*, to appear.

3. Gatteschi L. and C. Giordano, *Error bounds for McMahon's asymptotic
approximations of the zeros of the Bessel functions*, Integral Transforms
and Special Functions, to appear.

See latex file of the abstract.