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On computation of multiple zeros of derivatives of the cylindrical Bessel functions $J\sb{\nu}(z)$ and $Y\sb{\nu}(z)$. (Russian) Zbl 0588.65015
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.
Reviewer: S.Hitotumatu

65D20Computation of special functions, construction of tables
65H05Single nonlinear equations (numerical methods)
33C10Bessel and Airy functions, cylinder functions, ${}_0F_1$