Monotonicity of the Zeros of a Cross-Product of Bessel Functions

descriptionPublicationkeyboard_double_arrow_right Article 01 Aug 1978 English Publisher:Society for Industrial & Applied Mathematics (SIAM)Journal:SIAM Journal on Mathematical Analysis, volume 9, pages 759-767 (issn: 0036-1410, eissn: 1095-7154,

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Authors: Ismail, Mourad E. H.; Muldoon, Martin E.;

doi: 10.1137/0509055

Monotonicity of the Zeros of a Cross-Product of Bessel Functions

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Abstract

Our principal result is that for fixed $\beta (0 0$, the positive zeros of the cross-product \[J_{\nu + \beta } (x)K_\nu (\alpha x) - \alpha ^\beta J_\nu (x)K_{\nu + \beta } (\alpha x)\] increase with $\nu $, ${{ - \beta } / {2 \leqq \nu 1$.

Keywords

Bessel and Airy functions, cylinder functions, ${}_0F_1$

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