论文标题
抛物线缸和韦伯方程溶液的均匀渐近扩展
Uniform asymptotic expansions for solutions of the parabolic cylinder and Weber equations
论文作者
论文摘要
渐近膨胀是用于抛物线缸和韦伯微分方程的溶液的。另外，对于多项式强迫术语，考虑了方程式的不均匀版本。这些扩展涉及指数，通风和得分手功能，并缓慢地变化涉及简单系数的分析系数函数。对于参数的大值以及参数的无界真实和复杂值，近似值均匀地有效。具有明确且易于计算的误差边界，要么提供或用于所有近似值。
Asymptotic expansions are derived for solutions of the parabolic cylinder and Weber differential equations. In addition the inhomogeneous versions of the equations are considered, for the case of polynomial forcing terms. The expansions involve exponential, Airy and Scorer functions and slowly varying analytic coefficient functions involving simple coefficients. The approximations are uniformly valid for large values of the parameter and unbounded real and complex values of the argument. Explicit and readily computable error bounds are either furnished or available for all approximations.
