On the complex zeros of Hμ(z), J(z), J(z) for real or complex order |
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Authors: | C. G. Kokologiannaki and P. D. Siafarikas C. B. Kouris |
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Affiliation: | Department of Mathematics, University of Patras, Patras, Greece “Demokritos” National Research Center for Physical Sciences, Aghia Paraskevi Attikis, Athens, Greece |
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Abstract: | Propositions about the nonexistence of complex zeros of the functions Hμ(z)=Jμ(z)+zJ′μ(z),J′μ(z),J″μ(z), where J′μ(z) and J″μ(z) are the first two derivatives of the Bessel functions Jμ(z), for μ in general complex are proved. Bounds for the purely imaginary zeros of the above functions assuming their existence are given. Thus for the range of values for which these bounds are violated there are no purely imaginary zeros of the above functions. Finally, some known results from previous work are generalized in the present paper. |
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Keywords: | Mixed Bessel functions zeros of derivatives of Bessel functions |
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