Asymptotic expansions of integrals: the term by term integration method
نویسنده
چکیده
The classical term by term integration technique used for obtaining asymptotic expansions of integrals requires the integrand to have an uniform asymptotic expansion in the integration variable. A modification of this method is presented in which the uniformity requirement is substituted by a much weaker condition. As we show in some examples, the relaxation of the uniformity condition provides the term by term integration technique a large range of applicability. As a consequence of this generality, Watson’s lemma and the integration by parts technique applied to Laplace’s and a special family of Fourier’s transforms become corollaries of the term by term integration method.
منابع مشابه
Asymptotic expansions of integrals: The term-by-term integration method
The classical term-by-term integration technique used for obtaining asymptotic expansions of integrals requires the integrand to have an uniform asymptotic expansion in the integration variable. A modi cation of this method is presented in which the uniformity requirement is substituted by a much weaker condition. As we show in some examples, the relaxation of the uniformity condition provides ...
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