Asymptotic expansions of oscillatory integrals with complex phase

2009/03/20 by Robin Pemantle, Mark Wilson, Mark C. Wilson +2
Mathematics · #Algebraic and Geometric Analysis #Mathematical functions and polynomials #advanced mathematical theories #math.CO #msc:41A60

paper · pdf · doi:10.48550/arxiv.0903.3585

arxiv created 2009/03/20 · arxiv updated 2009/12/01

Abstract

We consider saddle point integrals in d variables whose phase function is neither real nor purely imaginary. Results analogous to those for Laplace (real phase) and Fourier (imaginary phase) integrals hold whenever the phase function is analytic and nondegenerate. These results generalize what is well known for integrals of Laplace and Fourier type. The method is via contour shifting in complex d-space. This work is motivated by applications to asymptotic enumeration.

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