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asymptotic methods


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1: 12.16 Mathematical Applications
2: Nico M. Temme
His book Asymptotic Methods for Integrals was published by World Scientific in 2015. …
3: 12.17 Physical Applications
Problems on high-frequency scattering in homogeneous media by parabolic cylinders lead to asymptotic methods for integrals involving PCFs. …
4: Roderick S. C. Wong
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 Lecture Notes on Applied Analysis, published by World Scientific in 2010. …
  • 5: Bibliography T
  • N. M. Temme (1992b) Asymptotic inversion of the incomplete beta function. J. Comput. Appl. Math. 41 (1-2), pp. 145–157.
  • N. M. Temme (1996a) Uniform asymptotics for the incomplete gamma functions starting from negative values of the parameters. Methods Appl. Anal. 3 (3), pp. 335–344.
  • N. M. Temme (2015) Asymptotic Methods for Integrals. Series in Analysis, Vol. 6, World Scientific Publishing Co. Pte. Ltd., Hackensack, NJ.
  • 6: 2.3 Integrals of a Real Variable
    This result is probably the most frequently used method for deriving asymptotic expansions of special functions. …
    §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
    Furthermore, as t 0 + , q ( t ) has the expansion (2.3.7). …
    §2.4(iii) Laplace’s Method
    Paths on which ( z p ( t ) ) is constant are also the ones on which | exp ( z p ( t ) ) | 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
    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. …
    §2.10(iv) Taylor and Laurent Coefficients: Darboux’s Method
    See also Flajolet and Odlyzko (1990).
    9: Frank W. J. Olver
    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. … 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. …
  • 10: 2.9 Difference Equations
    For applications of asymptotic methods for difference equations to orthogonal polynomials, see, e. …