Analytic continuation with respect to a~parameter of the Green's functions of exterior boundary value problems for the two-dimensional Helmholtz equation.~I

L. A. Muravei

Sbornik. Mathematics, Tome 26 (1975) no. 3, pp. 373-402

Résumé

In the first part of the paper one studies the distribution in the half-plane $\{\nu:|{\arg\nu}|\pi/2\}$ of the roots of the functions $H_\nu'(k)$ and $H_\nu'(k)+igH_\nu(k)$ and of the variable $\nu$ for arbitrary fixed complex $k$ from the region $K(\delta,\varkappa)=\{k:-\delta\arg k\pi/2-\delta,\ \varkappa|k|\}$ for some $\delta\in(0,\pi/2)$ and $\varkappa>0$, where $H_\nu(k)$ is the first Hankel function, $H_\nu'(k)$ is its derivative with respect to $k$, and $g$ is an arbitrary nonnegative number. Figures: 4. Bibliography: 10 titles.