The zeros of modified bessel functions as functions of their order

Mamedova A., Khanmamedov A. K.

Transactions Issue Mathematics, Azerbaijan National Academy of Sciences, vol.41, no.1, pp.133-137, 2021 (Scopus) identifier

  • Publication Type: Article / Article
  • Volume: 41 Issue: 1
  • Publication Date: 2021
  • Journal Name: Transactions Issue Mathematics, Azerbaijan National Academy of Sciences
  • Journal Indexes: Scopus
  • Page Numbers: pp.133-137
  • Keywords: Bessel functions, Eigenvalues, Schrödinger equation, Zeros of Bessel functions
  • Azerbaijan State University of Economics (UNEC) Affiliated: Yes

Abstract

Zeros of the function aKν (z) + bK′ν (z) considered as a function of the order are studied, where Kν (z) is the modified Bessel function of the second kind (Macdonald function). It is proved that, for fixed z, z > 0 and for any real values a, b, the function aKν (z) + bK′ν (z) has only a countable number of simple purely imaginary zeros νn. The asymptotics of the zeros νn as n → +∞ is found.