Kerimov, M. K.; Skorokhodov, S. L. On computation of multiple zeros of derivatives of the cylindrical Bessel functions \(J_{\nu}(z)\) and \(Y_{\nu}(z)\). (Russian) Zbl 0588.65015 Zh. Vychisl. Mat. Mat. Fiz. 25, No. 12, 1749-1760 (1985). 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 Cited in 2 ReviewsCited in 2 Documents 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, \({}_0F_1\) Keywords:multiple zero; derivatives of Bessel functions; computation of zeros; asymptotic formulas; Taylor expansion PDFBibTeX XMLCite \textit{M. K. Kerimov} and \textit{S. L. Skorokhodov}, Zh. Vychisl. Mat. Mat. Fiz. 25, No. 12, 1749--1760 (1985; Zbl 0588.65015) Digital Library of Mathematical Functions: Multiple Zeros ‣ §10.74(vi) Zeros and Associated Values ‣ §10.74 Methods of Computation ‣ Computation ‣ Chapter 10 Bessel Functions 10th item ‣ Real Zeros ‣ §10.75(iii) Zeros and Associated Values of the Bessel Functions, Hankel Functions, and their Derivatives ‣ §10.75 Tables ‣ Computation ‣ Chapter 10 Bessel Functions