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Zbl 0588.65015
Kerimov, M.K.; Skorokhodov, S.L.
On computation of multiple zeros of derivatives of the cylindrical Bessel functions $J\sb{\nu}(z)$ and $Y\sb{\nu}(z)$. (Russian)
[J] Zh. Vychisl. Mat. Mat. Fiz. 25, No.12, 1749-1760 (1985). ISSN 0044-4669

The authors discuss the multiple (actually double) zeros of the first to third derivatives of $J\sb{\nu}(z)$ and $Y\sb{\nu}(z)$ with real parameter $\nu$. They first refer previous works since J. Lense (1932/33). Due to Bessel's differential equation and its derivatives, we have easily a necessary condition and asymptotic formulas of z and $\nu$ for double zeros of the functions $J'\sb{-\nu}(z)$, $Y'\sb{-\nu}(z)$, $J''\sb{-\nu}(z)$, $Y''\sb{-\nu}(z)$ and $Y'''\sb{-\nu}(z)$. Starting from the asymptotic value in each interval between two consecutive integers $[n,n+1]$, they compute the numerical values of $\nu$ and z, using Taylor expansion in two variables $\nu$ and z. They also give several tables for the results.
[S.Hitotumatu]

MSC 2000:: *65D20 Computation of special functions
65H05 Single nonlinear equations (numerical methods)
33C10 Cylinder functions, etc.

Keywords: multiple zero; derivatives of Bessel functions; computation of zeros; asymptotic formulas; Taylor expansion

Cited in: Zbl 0611.33010 Zbl 0606.65011

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