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Approximation for the turning points of Bessel functions. (English) Zbl 0616.65016
Using Cayley’s algorithm for the numerical calculation of the zeros of oscillating functions, series approximations for $j'\sb{\nu,s}$, the sth turning point of the Bessel function of the first kind $J\sb{\nu}(x)$, i.e. the sth positive zero of $J'\sb{\nu}(x)$, $\nu >0$ are obtained in this paper, Chebyshev series approximations for $j'\sb{\nu,s}$, $0\le \nu \le 5$, $s=1,2,3,4,5$ and 6 are also presented.
Reviewer: C.L.Koul
65D20Computation of special functions, construction of tables
65H05Single nonlinear equations (numerical methods)
41A58Series expansions (e.g. Taylor, Lidstone series, but not Fourier series)
33C10Bessel and Airy functions, cylinder functions, ${}_0F_1$
30C15Zeros of polynomials, etc. (one complex variable)
Full Text: DOI
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[5] Olver, F. W. J.: Royal society mathematical tables, Bessel functions. 7 (1960)
[6] Piessens, R.: J. comput. Phys.. 53, 188 (1984)
[7] Piessens, R.: Math. comput.. 42, 195 (1984)