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An upper bound for the zeros of the derivative of Bessel functions |
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| Authors: | Árpád Elbert Andrea Laforgia |
| Affiliation: | 1. Mathematical Institute of the Hungarian Academy of Sciences, P.O.B. 127, H-1364, Budapest, Hungary 2. Dipartimento di Meccanica e Automatica, Terza Università di Roma, Via Corrado Segre, 2, 00146, Roma, Italia |
| Abstract: | Letj vk ′ denotes thekth positive zero of the derivativeJ v ′ (x)=dJ v (x)/dx of Bessel functionJ v (x) fork=1, 2,…. We establish the upper bound $$j'_{nu k}< nu + a_k left( {nu + frac{{{rm A}_k^3 }}{{a_k^3 }}} right)^{frac{1}{3}} + frac{3}{{10}}a_k^2 left( {nu + frac{{A_k^3 }}{{a_k^3 }}} right)^{frac{1}{3}} , nu geqslant 0, k = 1,2, ldots $$ |
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