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Monotonicity and complete monotonicity of some functions involving the modified Bessel functions of the second kind.
- Source :
-
Comptes Rendus. Mathématique . 2023, Vol. 361, p217-235. 19p. - Publication Year :
- 2023
-
Abstract
- In this paper, we introduce some monotonicity rules for the ratio of integrals. Furthermore, we demonstrate that the function -- Tν, α β(s) is completely monotonic in s and absolutely monotonic in ν if and only if β 1, where Tν, α β(s) = Kν²(s) -- βKν-α(s)Kν+α(s) defined on s > 0 and Kν(s) is the modified Bessel function of the second kind of order ν. Finally, we determine the necessary and sufficient conditions for the functions s → Tµ,α1(s)/Tν, α,1(s), s → (Tν, α,1(s))/(2T(µ+ν)/2,α,1(s)), and ... Tν, α,1(s)/... ν, α,1 (s) to be monotonic in s ∈ (0, ∞) by employing the monotonicity rules. [ABSTRACT FROM AUTHOR]
- Subjects :
- *BESSEL functions
*INTEGRALS
Subjects
Details
- Language :
- English
- ISSN :
- 1631073X
- Volume :
- 361
- Database :
- Academic Search Index
- Journal :
- Comptes Rendus. Mathématique
- Publication Type :
- Academic Journal
- Accession number :
- 175255425
- Full Text :
- https://doi.org/10.5802/crmath.399