Journal of Computational and Applied Mathematics
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,
Hyperasymptotic evaluation of the Pearcey integral via Hadamard expansions
Journal of Computational and Applied Mathematics - Special issue: International conference on mathematics and its application
Journal of Computational and Applied Mathematics
High-precision evaluation of the Bessel functions via Hadamard series
Journal of Computational and Applied Mathematics
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This paper is one of a series considering the application of Hadamard expansions in the hyperasymptotic evaluation of Laplace-type integrals of the form @!"Cexp{-z@j(t)}f(t)dt for large values of |z|. It is shown how the procedure can be employed to deal with the case when the amplitude function f(t) possesses poles which may coalesce with a saddle point of the integrand or approach the integration path C. A novel feature introduced here is the reverse-expansion procedure. This results in contributions at each exponential level (after the first) of the expansion in the form of rapidly convergent series, thereby enabling the high-precision evaluation of the above integral in coalescence problems. Numerical examples are given to illustrate the procedure.