On Zeros of the Modified Bessel Function of the First Kind

Khanmamedov A. K., Abbasova K. E.

AZERBAIJAN JOURNAL OF MATHEMATICS, vol.11, no.2, pp.176-182, 2021 (ESCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 11 Issue: 2
  • Publication Date: 2021
  • Journal Name: AZERBAIJAN JOURNAL OF MATHEMATICS
  • Journal Indexes: Emerging Sources Citation Index (ESCI), Scopus, Academic Search Premier, zbMATH
  • Page Numbers: pp.176-182
  • Azerbaijan State University of Economics (UNEC) Affiliated: Yes

Abstract

Zeros of the modified Bessel function I-nu (z) of the first kind, considered as a function of index nu are studied. It is proved that for each epsilon, epsilon > 0 outside the band vertical bar Im nu vertical bar < epsilon the function I-nu (z) can only have a finite number of zeros. Real zeros of the function I-nu (z) are located in the intervals (-2k, - (2k - 1)) , k = 1, 2, ....