Asymptotic solutions are derived for inhomogeneous differential equations having a large real or complex parameter and a simple turning point. They involve Scorer functions and three slowly varying analytic coefficient functions. The asymptotic approximations are uniformly valid for unbounded complex values of the argument, and are applied to inhomogeneous Airy equations having polynomial and exponential forcing terms. Error bounds are available for all approximations, including new simple ones for the well-known asymptotic expansions of Scorer functions of large complex argument.

中文翻译：

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具有转折点的非齐次微分方程的渐近解

对于具有较大实数或复数参数和简单转折点的非齐次微分方程，推导出渐近解。它们涉及 Scorer 函数和三个缓慢变化的解析系数函数。渐近近似对于参数的无界复数值一致有效，并且适用于具有多项式和指数强迫项的非齐次艾里方程。误差界限可用于所有近似，包括用于大复杂参数的 Scorer 函数的众所周知的渐近展开的新的简单的。