Miniaturized tables of Bessel functions. II

Abstract:

In a previous study, we discussed the expansion of two-parameter functions in a double series of Chebyshev polynomials, and, in particular, we presented coefficients for the evaluation of the modified Bessel function ${(2z/\pi )^{1/2}}{e^z}{K_v}(z)$ to 20 decimals for all $z \geqq 5$ and all $v,0 \leqq v \leqq 1$. In the present study, we give similar coefficients for the evaluation of $g{e^{ - z}}{z^{ - \mu }}{I_v}(z)$ to at least 20 decimals where ${I_v}(z)$ is the modified Bessel function of the first kind and g and $\mu$ are certain constants which depend on the range of the parameter and variable for four different situations. The ranges are $(1)\;0 < z \leqq 8,0 \leqq v \leqq 4;(2)\;0 < z \leqq 8,4 \leqq v \leqq 8;(3)\;z \geqq 8, - 1 \leqq v \leqq 0;(4)\;z \geqq 8,0 \leqq v \leqq 1$.