Title: Asymptotic relation for zeros of cross-product of Bessel functions and applications Authors: Bobkov, Vladimír Citation: BOBKOV, V. Asymptotic relation for zeros of cross-product of Bessel functions and applications. Journal of Mathematical Analysis and Applications, 2019, roč. 472, č. 1, s. 1078-1092. ISSN 0022-247X. Issue Date: 2019 Publisher: Elsevier Document type: článekarticle URI: 2-s2.0-85057886086http://hdl.handle.net/11025/31264 ISSN: 0022-247X Keywords in different language: cross-product of Bessel functions;asymptotic of zeros;upper bound for zeros;Bessel functions;eigenvalues;Pleijel theorem Abstract in different language: Let $a_{\nu,k}$ be the $k$-th positive zero of the cross-product of Bessel functions $J_\nu(R z) Y_\nu(z) - J_\nu(z) Y_\nu(R z)$, where $\nu\geq 0$ and $R>1$. We derive an initial value problem for a first order differential equation whose solution $\alpha(x)$ characterizes the limit behavior of $a_{\nu,k}$ in the following sense: $$\lim_{k \to \infty} \frac{a_{kx,k}}{k} = \alpha(x), \quad x \geq 0.$$ Moreover, we show that $$a_{\nu,k} < \frac{\pi k}{R-1} + \frac{\pi \nu}{2 R}.$$ We use $\alpha(x)$ to obtain an explicit expression of the Pleijel constant for planar annuli and compute some of its values. Rights: © Elsevier Appears in Collections: Články / Articles (NTIS)OBD

Files in This Item:
File SizeFormat
Please use this identifier to cite or link to this item: http://hdl.handle.net/11025/31264