Approximation for the turning points of Bessel functions (Q1821490)

Using Cayley's algorithm for the numerical calculation of the zeros of oscillating functions, series approximations for \(j'_{\nu,s}\), the sth turning point of the Bessel function of the first kind \(J_{\nu}(x)\), i.e. the sth positive zero of \(J'_{\nu}(x)\), \(\nu >0\) are obtained in this paper, Chebyshev series approximations for \(j'_{\nu,s}\), \(0\leq \nu \leq 5\), \(s=1,2,3,4,5\) and 6 are also presented.