Asymptotic relation for zeros of cross-product of Bessel functions and applications

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F49777513%3A23520%2F19%3A43953960" target="_blank" >RIV/49777513:23520/19:43953960 - isvavai.cz</a>
Result on the web
<a href="https://www.sciencedirect.com/science/article/pii/S0022247X18310114" target="_blank" >https://www.sciencedirect.com/science/article/pii/S0022247X18310114</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.jmaa.2018.11.065" target="_blank" >10.1016/j.jmaa.2018.11.065</a>

Result language
angličtina
Original language name
Asymptotic relation for zeros of cross-product of Bessel functions and applications
Original language description
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 $nugeq 0$ 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.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics

Project
Result was created during the realization of more than one project. More information in the Projects tab.
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2019
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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