On a product of modified Bessel functions

Research output: Contribution to journalArticle

33 Citations (Scopus)

Abstract

Let I v and K v denote the modified Bessel functions of the first and second kinds of order v. In this note we prove that the monotonicity of u I v(u)K v(u)on(0, ∞)for all v≥-1/2 is an almost immediate consequence of the corresponding Turán type inequalities for the modified Bessel functions of the first and second kinds of order v. Moreover, we show that the function u I v(u)K v(u) is strictly completely monotonic on (0, ∞) for all v ∈ [-1/2,1/2]. At the end of this note, a conjecture is stated.

Original languageEnglish
Pages (from-to)189-193
Number of pages5
JournalProceedings of the American Mathematical Society
Volume137
Issue number1
DOIs
Publication statusPublished - Jan 2009

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Neumann function
Bessel function of the first kind
Modified Bessel Functions
Bessel functions
Monotonic
Monotonicity
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Keywords

  • Complete monotonicity
  • Modified Bessel functions
  • Turán type inequalities

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

Cite this

On a product of modified Bessel functions. / Baricz, A.

In: Proceedings of the American Mathematical Society, Vol. 137, No. 1, 01.2009, p. 189-193.

Research output: Contribution to journalArticle

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