Bounds for the first positive zero of a mixed Bessel function (Q1113617)

Let \(\alpha\), \(\nu\) be given real numbers, \(x\in {\mathbb{R}}\), \(x\mapsto J_{\nu}(x)\) the Bessel function of order \(\nu\) and \(x\mapsto J'_{\nu}=dJ_{\nu}(x)/dx\) its derivative. The authors present new upper and lower bounds for the first positive zero of the function \(x\mapsto \alpha J_{\nu}(x)+xJ'_{\nu}(x)\) when \(\nu >-1\).