Asymptotic expansion of oscillatory integrals with singular phases

Abstract

The purpose of this article is to describe the singularities of one-dimensional oscillatory integrals, whose phases have a certain singularity, in the form of an asymptotic expansion. In the case of the Laplace integral, an analogous result is also given.

References in corpus (3)

• Generalized Fresnel integrals as oscillatory integrals with positive real power phase functions and applications to asymptotic expansions
• On asymptotic expansions of oscillatory integrals with phase functions expressed by a product of positive real power function and real analytic function in one variable
• Oscillatory integrals with phase functions of positive real powers and asymptotic expansions