Bounds on differences of adjacent zeros of Bessel functions and iterative relations between consecutive zeros期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

Bounds on differences of adjacent zeros of Bessel functions and iterative relations between consecutive zeros

Authors:	Javier Segura.

Affiliation:	Instituto de Bioingeniería, Universidad Miguel Hernández, Edificio La Galia, 03202-Elche, Alicante, Spain

Abstract:	Bounds for the distance $vert c_{nu ,s}-c_{nu pm 1 , s^{prime}}vert$ between adjacent zeros of cylinder functions are given; and $s^{prime}$ are such that $nexists c_{nu,s^{primeprime}}in ]c_{nu ,s},c_{nupm 1,s^{prime}}[$ ; $c_{nu ,k}$ stands for the th positive zero of the cylinder (Bessel) function $mathcal{C}_{nu}(x)=cosalpha J_{nu}(x) - sinalpha Y_{nu}(x)$ , , . These bounds, together with the application of modified (global) Newton methods based on the monotonic functions $f_{nu}(x)=x^{2nu -1}mathcal{C}_{nu}(x)/mathcal{C}_{nu -1}(x)$ and $g_{nu}(x)=-x^{-(2nu +1)}mathcal{C}_{nu}(x)/mathcal{C}_{nu +1}(x)$ , give rise to forward ( $c_{nu ,k} rightarrow c_{nu ,k+1}$ ) and backward ( $c_{nu ,k+1} rightarrow c_{nu ,k}$ ) iterative relations between consecutive zeros of cylinder functions. The problem of finding all the positive real zeros of Bessel functions $mathcal{C}_{nu}(x)$ for any real and inside an interval $[x_{1},x_{2}]$ , $x_{1}>0$ , is solved in a simple way.

Keywords:	Bessel functions cylinder functions adjacent and consecutive zeros global Newton method

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