Asymptotic Expansion of Integrals
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.
KeywordsSaddle Point Asymptotic Expansion Integral Representation Steep Descent Local Analysis
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- 26.Copson, E. T., Asymptotic Expansions, Cambridge University Press, Cambridge, 1967.Google Scholar
- 27.Olver, F. W. J., Asymptotics and Special Functions, Academic Press, Inc., New York, 1974.Google Scholar
- 28.See also Refs. 15 to 17. Integral representations of special functions are given in Refs. 10 to 12 and: Gradshteyn, I. S., and Ryzhik, I. W., Tables of Integrals, Series, and Products, 4th ed., Academic Press, Inc., New York, 1965.Google Scholar