On the zeros of derivatives of Bessel functions |
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Authors: | Árpád Elbert Andrea Laforgia |
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Affiliation: | 1. Mathematical Institute of the Hungarian Academy of Sciences, P.f. 428, 1376, Budapest, Hungary 2. Dipt. di Matematica dell'Universitá, Via Carlo Alberto 10, 10123, Torino, Italy
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Abstract: | In this paper we are interested in the behaviour respect tov of thekth positive zeroc′ vk of the derivative of the general Bessel functionC v(x)=J v(x)cosα?Y v(x)sinα, 0≤α<π, whereJ v(x) andY v(x) indicate the Bessel functions of first and second kind respectively. It is well known that forc′ vk>∥v∥,c′ vk increases asv increases. Here we prove several additional properties forc′ vk. Our main result is thatc′ vk is concave as a function ofv, whenc′ vk>∥v∥>0. This implies the concavity ofc′ vk for everyk=2,3, ?. In the case of the zerosJ′ vk of d dx J v(x) we extend this property tok=1 for everyv≥0. |
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