On the zeros of the Macdonald functions

TL;DR

This paper investigates the zeros of Macdonald functions (modified Bessel functions of the second kind) with real index, analyzing their behavior as the index varies and supporting findings with numerical computations.

Contribution

It provides a detailed description of how the zeros of Macdonald functions change with the index, including explicit algebraic equations and numerical analysis.

Findings

Zeros' behavior described as index varies

Explicit algebraic equations for zeros derived

Numerical computations support theoretical results

Abstract

We are concerned with the zeros of the Macdonald functions or the modified Bessel functions of the second kind with real index. By using the explicit expressions for the algebraic equations satisfied by the zeros, we describe the behavior of the zeros when the index moves. Results by numerical computations are also presented.