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Interlacing of positive real zeros of Bessel functions. (English) Zbl 1208.33007
The positive zeros j ν,s , y ν,s , j ν,s ' , y ν,s ' , j ν+ε,s , y ν+ε,s , s=1,2,, of Bessel functions J ν (x), Y ν (x), J ν ' (x), Y ν ' (x), J ν+ε (x), Y ν+ε (x), respectively, interlace according the inequalities: j ν,s ' <y ν,s <y ν+ε,s <y ν,s ' <j ν,s <j ν+ε,s <j ν,s+1 ' <, s=1,2,, for ν0 and 0<ε1. For ε=1, analogous results are widely known.
33C10Bessel and Airy functions, cylinder functions, 0 F 1
34C10Qualitative theory of oscillations of ODE: zeros, disconjugacy and comparison theory
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[2]Pálmai, T.; Apagyi, B.: On nonsingular potentials of Cox-Thompson inversion scheme, J. math. Phys. 51, 022114 (2010)
[3]Watson, G. N.: A treatise on the theory of Bessel functions, Cambridge math. Lib. (1995)
[4]Liu, H. Y.; Zou, J.: Zeros of the Bessel and spherical Bessel functions and their applications for uniqueness in inverse acoustic obstacle scattering, IMA J. Appl. math. 72, 817-831 (2007) · Zbl 1138.35072 · doi:10.1093/imamat/hxm013
[5]H.Y. Liu, J. Zou, Zeros of the Bessel and spherical Bessel functions and their applications for uniqueness in inverse acoustic obstacle scattering problems, Technical Report CUHK-2007-02 (342), The Chinese University of Hong Kong, Hong Kong, 2007.