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On the coefficients that arise from Laplace’s method. (English) Zbl 1096.41008
The author studies the extensions to Erdélyi’s theorem on many types of integrals including the Laplace transform. It’s essential in the method of steepest descent. He shows that the coefficients in any particular application and clarify the theoretical basis of Erdélyi’s expansion: it turns out that Faà di Bruno’s formula has always played a central role in it. He studies an example and gives an open problem about this theme.

MSC:
41A10 Approximation by polynomials
41A60 Asymptotic approximations, asymptotic expansions (steepest descent, etc.)
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