On the $\nu$zeros of the modified Bessel function $K_{i\nu}(x)$ of positive argument
Abstract
The modified Bessel function of the second kind $K_{i\nu}(x)$ of imaginary order for fixed $x>0$ possesses a countably infinite sequence of real zeros. Recently it has been shown that the $n$th zero behaves like $\nu_n\sim \pi n/\log\,n$ as $n\to\infty$. In this note we determine a more precise estimate for the bahaviour of these zeros for large $n$ by making use of the known asymptotic expansion of $K_{i\nu}(x)$ for large $\nu$. Numerical results are presented to illustrate the accuracy of the expansion obtained.
 Publication:

arXiv eprints
 Pub Date:
 August 2021
 DOI:
 10.48550/arXiv.2108.01447
 arXiv:
 arXiv:2108.01447
 Bibcode:
 2021arXiv210801447P
 Keywords:

 Mathematics  Classical Analysis and ODEs;
 33C10;
 34E05;
 41A30;
 41A60
 EPrint:
 6 pages, 1 figure