Numerical methods for the computation of the parabolic cylinder $U(a,z)$ for real $a$ and complex $z$ are presented. The main tools are recent asymptotic expansions involving exponential and Airy functions, with slowly varying analytic coefficient functions involving simple coefficients, and stable integral representations; these two main main methods can be complemented with Maclaurin series and a Poincar\'e asymptotic expansion. We provide numerical evidence showing that the combination of these methods is enough for computing the function with $5\times 10^{-13}$ relative accuracy in double precision floating point arithmetic.

翻译：提出了实际美元和复杂美元(a,z)美元对抛光圆柱的数值计算方法,主要工具是最近涉及指数函数和空气函数的无症状扩展,分析系数函数缓慢变化,涉及简单系数,以及稳定的整体表示;这两种主要方法可以用Maclaurin系列和Poincar\'e无症状扩展加以补充。我们提供了数字证据,表明这些方法的结合足以用5美元乘以10 ⁇ -13美元相对精确的双精度浮点算法计算函数。