Mathematical Sciences: Uniform Asymptotic Expansion of Integrals

这项研究将考虑与以下方面有关的几个问题： 由积分定义的函数的渐近展开式。 实际的误差界将构造一致渐近 相关的大次勒让德函数的展开式， 固定顺序直接从这些积分表示 功能协调发展的 切斯特、弗里德曼和厄塞尔的经典方法 将通过将相函数映射到有理 功能和功能。 可计算误差的推导 边界将被强调。 这项工作在特殊功能领域的应用。 这些功能在各种物理环境中非常自然地出现。 在流体力学和固体力学的背景下。

This research will consider several problems associated with the asymptotic expansions of functions defined by integrals. Realistic error bounds will be constructed for uniform asymptotic expansions of associated Legendre functions of large degree and fixed order directly from the integral representations of these functions. The classical method of Chester, Friedman, and Ursell will be generalized by mapping phase functions into rational functions and logarithms. The derivation of computable error bounds will be emphasized. This work has applications in the area of special functions. Such functions arise quite naturally in a variety of physical contexts in both fluid dynamics and solid mechanics.