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Zeitschrift für Analysis und ihre Anwendungen


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Volume 10, Issue 4, 1991, pp. 563–567
DOI: 10.4171/ZAA/477

Published online: 1991-12-31

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

C.G. Kokologiannaki[1] and P.D. Siafarikas

(1) University of Patras, Greece

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.

Keywords: Complex zeros, purely imaginary zeros, Bessel functions

Kokologiannaki C.G., Siafarikas P.D.: Non-Existence of Complex and Purely Imaginary Zeros of a Transcendental Equation Involving Bessel Functions. Z. Anal. Anwend. 10 (1991), 563-567. doi: 10.4171/ZAA/477