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Hyperasymptotic evaluation of the Pearcey integral via Hadamard expansions |
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| Authors: | RB Paris D Kaminski |
| Institution: | aDivision of Mathematical Sciences, University of Abertay Dundee, Dundee DD1 1HG, UK bDepartment of Mathematics & Computer Science, University of Lethbridge, Lethbridge, Alberta, Canada T1K 3M4 |
| 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. |
| Keywords: | Pearcey integral Hyperasymptotics Hadamard expansions Caustic curve Stokes set |
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