On the power of the zeros of Bessel functions |
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| Authors: | Árpád Elbert Andrea Laforgia |
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| Institution: | 1. Mathematical Institute of the Hungarian, Academy of Sciences, P.f. 428, 1376, Budapest, Hungary
2. Dipartimento di Matematica ed Applicazioni, Università di Palermo, Via Archirafi, 34, 90123, Palermo, (Italy)
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| Abstract: | For ν≥0 let cνk be the k-th positive zero of the cylinder functionC v(t)=J v(t)cosα-Y v(t)sinα, 0≤α>π whereJ ν(t) andY ν(t) denote the Bessel functions of the first and the second kind, respectively. We prove thatC v,k 1+H(x) is convex as a function of ν, ifc νk≥x>0 and ν≥0, whereH(x) is specified in Theorem 1.1. |
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