具有转向点的非齐次微分方程的渐近解
Asymptotic solutions of inhomogeneous differential equations having a turning point
摘要：
导出了具有大实参数或复参数和简单转向点的非齐次微分方程的渐近解。它们涉及得分函数和三个缓慢变化的解析系数函数。渐近近似是一致有效的无界复值的参数，并适用于非齐次Airy方程的多项式和指数强迫项。误差界可用于所有的近似，包括新的简单的著名的渐近展开的得分函数的大复杂的参数。
英文摘要：
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.
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