论文标题
具有复杂参数的抛物线缸函数的计算
Computation of parabolic cylinder functions having complex argument
论文作者
论文摘要
提出了用于计算抛物线缸$ u（a，z）$的数值方法。主要工具是涉及指数和通风函数的近期渐近扩展，其分析系数函数涉及简单系数，并具有稳定的积分表示。这两种主要方法可以与麦克洛林系列和庞加莱渐近扩张相辅相成。我们提供的数值证据表明，这些方法的组合足以用$ 5 \ times 10^{ - 13} $在双精度浮点算术中计算功能。
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 Poincaré 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.
