# Non-Existence of Complex and Purely Imaginary Zeros of a Transcendental Equation Involving Bessel Functions

### C.G. Kokologiannaki

University of Patras, Greece### P.D. Siafarikas

University of Patras, Greece

## Abstract

Some results concerning the non-existence of complex and purely imaginary zeros of the transcendental equation $F(z)J_v(z)+G(z)J'_v(z) = 0$ are given, where $J_v(z)$ is the Bessel function of first kind and order $v$ (in general complex), $J'_v(z)$ is the derivative of $J_v(z)$, and $F(z)$, $G(z)$ are analytic functions. The obtained results improve and generalize previously known ones.

## Cite this article

C.G. Kokologiannaki, P.D. Siafarikas, Non-Existence of Complex and Purely Imaginary Zeros of a Transcendental Equation Involving Bessel Functions. Z. Anal. Anwend. 10 (1991), no. 4, pp. 563–567

DOI 10.4171/ZAA/477