Abstract:In the paper we consider integrals of form ∫︁ () exp[ () ln()] , where () is a smooth increasing function on the semi-axis [0, ∞) such that lim →+∞ () = ∞. We find a precise information on their asymptotic behavior and we prove an analogue of Riemann-Lebesgue lemma for trigonometric integrals. By applying this lemma, we succeed to obtain the asymptotic formulae for integrals with an absolutely continuous function. The proposed method of obtaining asymptotic formulae differs from classical method like Laplace m… Show more
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