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On the zeros of the Pearcey integral. (English) Zbl 0931.41018
From the authors’ summary: Zeros for real values of the arguments of the Pearcey integral are numerically evaluated and plotted. From this numerical examination, it is apparent that these zeroes display a high degree of structure, the character of which is revealed through asymptotic analysis.

41A60Asymptotic approximations, asymptotic expansions (steepest descent, etc.)
Full Text: DOI
[1] Berry, M. V.; Klein, S.: Colored diffraction catastrophes. Proc. natl. Acad. sci. USA 93, 2614-2619 (1996) · Zbl 0849.58008
[2] Connor, J. N. L.; Curtis, P. R.: A method for the numerical evaluation of the oscillatory integrals associated with the cuspoid catastrophes: application to pearcey’s integral and its derivatives. J. phys. A 15, 1179-1190 (1982) · Zbl 0485.65019
[3] Connor, J. N. L.; Curtis, P. R.; Farrelly, D.: The uniform asymptotic swallowtail approximation: practical methods for oscillating integrals with four coalescing saddle points. J. phys. A 17, 283-310 (1984) · Zbl 0534.65098
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[5] Kaminski, D.: Asymptotic expansion of the pearcey integral near the caustic. SIAM J. Math. anal. 20, No. 4, 987-1005 (1989) · Zbl 0674.33008
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