Hyperasymptotic evaluation of the Pearcey integral via Hadamard expansions

Authors:
R. B. Paris;D. Kaminski
Affiliations:
Division of Mathematical Sciences, University of Abertay Dundee, Dundee DD1 1HG, UK;Department of Mathematics & Computer Science, University of Lethbridge, Lethbridge, Alberta, Canada T1K 3M4
Venue:
Journal of Computational and Applied Mathematics
Year:
2006

Citing 4
Cited 0

Asymptotic expansion of the pearcey integral near the caustic

SIAM Journal on Mathematical Analysis
On the zeros of the Pearcey integral

Journal of Computational and Applied Mathematics
On the use of Hadamard expansions in hyperasymptotic evaluation of Laplace-type integrals: I: real variable

Journal of Computational and Applied Mathematics
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,

Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,

Quantified Score

Hi-index	7.29

Visualization

Abstract

We describe high-precision computations of the Pearcey integral Pe(x,y) for real x and y by means of Hadamard expansions. Numerical results for (x,y) situated in different regions of the x,y-plane are given to illustrate the levels of precision that can be achieved. Particular emphasis is given to computation in the neighbourhood of the two cusped curves associated with Pe(x,y) across which there is either a coalescence of saddles or a Stokes phenomenon.