Asymptotic Expansion of Integrals

Carl M. Bender and Steven A. Orszag
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Carl M. Bender: Washington University, Department of Physics
Steven A. Orszag: Yale University, Department of Mathematics

Chapter Chapter Six in Advanced Mathematical Methods for Scientists and Engineers I, 1999, pp 247-316 from Springer

Abstract: Abstract The analysis of differential and difference equations in Chaps. 3 to 5 is pure local analysis; there we predict the behavior of solutions near one point, but we do not incorporate initial-value or boundary-value data at other points. As a result, our predictions of the local behavior usually contain unknown constants. However, when the differential or difference equation is soluble, we can use the boundary and initial data to make parameter-free predictions of local behavior.

Keywords: Saddle Point; Asymptotic Expansion; Integral Representation; Steep Descent; Local Analysis (search for similar items in EconPapers)
Date: 1999
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DOI: 10.1007/978-1-4757-3069-2_6

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