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On computation of multiple zeros of derivatives of the cylindrical Bessel functions J ν (z) and Y ν (z). (Russian) Zbl 0588.65015
The authors discuss the multiple (actually double) zeros of the first to third derivatives of J ν (z) and Y ν (z) with real parameter ν. 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 ν for double zeros of the functions J -ν ' (z), Y -ν ' (z), J -ν '' (z), Y -ν '' (z) and Y -ν ''' (z). Starting from the asymptotic value in each interval between two consecutive integers [n,n+1], they compute the numerical values of ν and z, using Taylor expansion in two variables ν and z. They also give several tables for the results.
Reviewer: S.Hitotumatu

MSC:
65D20Computation of special functions, construction of tables
65H05Single nonlinear equations (numerical methods)
33C10Bessel and Airy functions, cylinder functions, 0 F 1