Asymptotic expansions of integrals: The term-by-term integration method

✍ Scribed by JoséL. López

• Publisher: Elsevier Science
• Year: 1999
• Tongue: English
• Weight: 982 KB
• Volume: 102
• Category: Article
• ISSN: 0377-0427
• DOI: 10.1016/s0377-0427(98)00216-7

✦ Synopsis

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.