关于纯虚级Bessel函数的$ν$ -零点
On the $ν$-zeros of the Bessel functions of purely imaginary order
摘要：
纯虚阶贝塞尔函数的$ν$ -零点被检查为固定参数$x>0$。在第二类修正贝塞尔函数$K_{iν}(x)$的情况下，已知它具有由$ν_n\sim πn/\log\,n$描述为$n\to\infty$的实数$ν$ -零的可数无穷序列。在这里，我们应用一个统一的方法来确定渐近估计的$ν$ -零的修改贝塞尔函数$L_{iν}(x)\equiv I_{iν}(x)+I_{-iν}(x)$和$K_{iν}(x)$和普通贝塞尔函数$J_{iν}(x)\pm J_{-iν}(x)$。
英文摘要：
The $ν$-zeros of the Bessel functions of purely imaginary order are examined for fixed argument $x>0$. In the case of the modified Bessel function of the second kind $K_{iν}(x)$, it is known that it possesses a countably infinite sequence of real $ν$-zeros described by $ν_n\sim πn/\log\,n$ as $n\to\infty$. Here we apply a unified approach to determine asymptotic estimates of the $ν$-zeros of the modified Bessel functions $L_{iν}(x)\equiv I_{iν}(x)+I_{-iν}(x)$ and $K_{iν}(x)$ and the ordinary Bessel functions $J_{iν}(x)\pm J_{-iν}(x)$.
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