Miniaturized tables of Bessel functions

Abstract:

In this report, we discuss the representation of bivariate functions in double series of Chebyshev polynomials. For an application, we tabulate coefficients which are accurate to 20 decimals for the evaluation of ${(2z/\pi )^{1/2}}{e^z}{K_v}(z)$ for all $z \geqq 5$ and all $v,0 \leqq v \leqq 1$. Since ${K_v}(z)$ is an even function in v and satisfies a three-term recurrence formula in v which is stable when used in the forward direction, we can readily evaluate ${K_v}(z)$ for all $z \geqq 5$ and all $v \geqq 0$. Only 205 coefficients are required to achieve an accuracy of about 20 decimals for the z and v ranges described. Extension of these ideas for the evaluation of all Bessel functions and other important bivariate functions is under way.