PreprintCC BY 4.0arXiv
On the log-concavity of the composite Bessel function $x^αJ_{ν}\left( βx^γ\right) $
Abstract
For a twice differentiable function f:( a,b) → ℝ define v( f) =f′f′−f′′ f. It is well known that the positivity of $v\left( f\right) $ implies that the function $\left\vert f\right\vert $ is strictly log-concave on each subinterval which does not contain zeros of f. In this paper we provide criteria for the positivity of $v\left( F\right) $ for the composite Bessel function $F\left( x\right) =J_{α,β,γ,ν}\left( x\right) :=x^αJ_ν\left( βx^γ\right) $ for positive numbers β and γ and real numbers α and ν.
Related
- Skew braces whose left series is not generated by right-normed star products
- On the exponential Diophantine equation (Pn(k))x+(Pr(k))x=Pm(k)
- On the exponential Diophantine equation (Pn+1(k))x−(Pn−1(k))x=2Pm(k)
- Infinite log-concavity of the Taylor coefficients of the Riemann xi-function
- The p-rationality of ℚ(√(−(kp+m))) and ℚ(√(p(p+1)))
BibTeX
@misc{kounchev2026logconcavity,
title = {{On the log-concavity of the composite Bessel function $x^αJ_ν\left( βx^γ\right) $}},
author = {O. Kounchev and H. Render},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.11158},
eprint = {2609.11158},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.11158},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - On the log-concavity of the composite Bessel function $x^αJ_{ν}\left( βx^γ\right) $
AU - O. Kounchev
AU - H. Render
PY - 2026
DA - 2026/09/10
PB - arXiv
DO - 10.48550/arxiv.2609.11158
UR - https://arxiv.org/abs/2609.11158
AB - For a twice differentiable function f:( a,b) → ℝ define v( f) =f^′f^′−f^′′ f. It is well known that the positivity of $v\left( f\right) $ implies that the function $\left\vert f\right\vert $ is strictly log-concave on each subinterval which does not contain zeros of f. In this paper we provide criteria for the positivity of $v\left( F\right) $ for the composite Bessel function $F\left( x\right) =J_{α,β,γ,ν}\left( x\right) :=x^αJ_ν\left( βx^γ\right) $ for positive numbers β and γ and real numbers α and ν.
ER -