论文标题
广义菲涅尔积分作为振荡积分，具有正真实功率相函数和渐近扩展的应用
Generalized Fresnel integrals as oscillatory integrals with positive real power phase functions and applications to asymptotic expansions
论文作者
论文摘要
在本文中，我们首先通过更改Cauchy积分定理在菲涅尔积分中进行集成的路径来概括菲涅尔积分。接下来，根据振荡的积分，我们还获得了扩展的菲涅尔积分的进一步概括。此外，通过使用此结果，我们具有具有正真实参数的振荡积分的渐近膨胀，对于由正面实际功率表达的退化临界点（包括中等振荡）和合适振幅函数的相位函数。该结果在一个变量中提供了固定相法的更细长的扩展，该方法被称为具有非分级临界点的相位函数的振荡积分的渐近扩展方法。
In this paper, we first generalize the Fresnel integrals by changing of a path for integration in the proof of the Fresnel integrals by Cauchy's integral theorem. Next, according to oscillatory integral, we also obtain further generalization of the extended Fresnel integrals. Moreover by using this result, we have an asymptotic expansion of an oscillatory integral with a positive real parameter, for a phase function with a degenerate critical point expressed by positive real power, including a moderate oscillation, and for a suitable amplitude function. This result gives a finer extension of the stationary phase method in one variable, which is known as a method for an asymptotic expansion of an oscillatory integral of a phase function with a non-degenerate critical point.
