# asymptotic methods

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## 1—10 of 74 matching pages

##### 1: 12.16 Mathematical Applications

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##### 2: Nico M. Temme

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►His book Asymptotic Methods for Integrals was published by World Scientific in 2015.
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##### 3: 12.17 Physical Applications

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►Problems on high-frequency scattering in homogeneous media by parabolic cylinders lead to asymptotic methods for integrals involving PCFs.
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##### 4: Roderick S. C. Wong

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►He is the author of the book Asymptotic Approximations of Integrals, published by Academic Press in 1989 and reprinted by SIAM in its Classics in Applied Mathematics Series in 2001, and of
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*Lecture Notes on Applied Analysis*, published by World Scientific in 2010. … ►##### 5: Bibliography T

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Asymptotic inversion of the incomplete beta function.
J. Comput. Appl. Math. 41 (1-2), pp. 145–157.
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Uniform asymptotics for the incomplete gamma functions starting from negative values of the parameters.
Methods Appl. Anal. 3 (3), pp. 335–344.
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Asymptotic Methods for Integrals.
Series in Analysis, Vol. 6, World Scientific Publishing Co. Pte. Ltd., Hackensack, NJ.
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##### 6: 2.3 Integrals of a Real Variable

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►This result is probably the most frequently used method for deriving asymptotic expansions of special functions.
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###### §2.3(iii) Laplace’s Method

… ►###### §2.3(iv) Method of Stationary Phase

… ►For extensions to oscillatory integrals with more general $t$-powers and logarithmic singularities see Wong and Lin (1978) and Sidi (2010). ►###### §2.3(v) Coalescing Peak and Endpoint: Bleistein’s Method

…##### 7: 2.4 Contour Integrals

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►Furthermore, as $t\to 0+$, $q(t)$ has the expansion (2.3.7).
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###### §2.4(iii) Laplace’s Method

… ►Paths on which $\mathrm{\Im}\left(zp(t)\right)$ is constant are also the ones on which $|\mathrm{exp}\left(-zp(t)\right)|$ decreases most rapidly. … ►###### §2.4(v) Coalescing Saddle Points: Chester, Friedman, and Ursell’s Method

… ►For a symbolic method for evaluating the coefficients in the asymptotic expansions see Vidūnas and Temme (2002). …##### 8: 2.10 Sums and Sequences

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►The asymptotic behavior of entire functions defined by Maclaurin series can be approached by converting the sum into a contour integral by use of the residue theorem and applying the methods of §§2.4 and 2.5.
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###### §2.10(iv) Taylor and Laurent Coefficients: Darboux’s Method

… ►See also Flajolet and Odlyzko (1990).##### 9: Frank W. J. Olver

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►In 1945–1961 he was a founding member of the Mathematics Division and Head of the Numerical Methods Section at the National Physical Laboratory, Teddington, U.
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►He is particularly known for his extensive work in the study of the asymptotic solution of differential equations, i.
…Having witnessed the birth of the computer age firsthand (as a colleague of Alan Turing at NPL, for example), Olver is also well known for his contributions to the development and analysis of numerical methods for computing special functions.
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##### 10: 2.9 Difference Equations

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►For applications of asymptotic methods for difference equations to orthogonal polynomials, see, e.
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