Miniaturized tables of Bessel functions. III

Abstract:

After the manner of our previous studies, coefficients for the expansion of ${J_\nu }(z)$ and ${Y_\nu }(z)$ in double series of Chebyshev polynomials are presented. For ${J_\nu }(z)$ the ranges are (1) $0 < z \leqq 8,0 \leqq \nu \leqq 4$, (2) $0 < z \leqq 8,4 \leqq \nu \leqq 8$. For ${J_\nu }(z) + i{Y_\nu }(z)$, the ranges are $z \geqq 5$ and $0 \leqq \nu \leqq 1$. The coefficients are given with sufficient accuracy to enable the evaluation of the Bessel functions to at least 20 decimals.