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Zbl 0616.65016
Piessens, Robert; Ahmed, Shafique
Approximation for the turning points of Bessel functions. (English)
[J] J. Comput. Phys. 64, 253-257 (1986). ISSN 0021-9991

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.
[C.L.Koul]

MSC 2000:: *65D20 Computation of special functions
65H05 Single nonlinear equations (numerical methods)
41A58 Series expansions
33C10 Cylinder functions, etc.
30C15 Zeros of polynomials, etc. (one complex variable)

Keywords: asymptotic expansions; Cayley's algorithm; zeros of oscillating functions; turning point; Bessel function; Chebyshev series approximations

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Zentralblatt MATH Berlin [Germany]