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On computation of multiple zeros of derivatives of the cylindrical Bessel functions \(J_{\nu}(z)\) and \(Y_{\nu}(z)\). (Russian) Zbl 0588.65015

The authors discuss the multiple (actually double) zeros of the first to third derivatives of \(J_{\nu}(z)\) and \(Y_{\nu}(z)\) 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 \(J'_{-\nu}(z)\), \(Y'_{-\nu}(z)\), \(J''_{-\nu}(z)\), \(Y''_{-\nu}(z)\) and \(Y'''_{-\nu}(z)\). 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

MSC:

65D20 Computation of special functions and constants, construction of tables
65H05 Numerical computation of solutions to single equations
33C10 Bessel and Airy functions, cylinder functions, \({}_0F_1\)
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