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Asymptotic expansions / E. T. Copson

Auteur principal : Copson, Edward Thomas, 1901-1980, AuteurType de document : MonographieCollection : Cambridge tracts in mathematics and mathematical physics, 55Langue : anglais.Pays : Grande Bretagne.Éditeur : London : Cambridge University Press, 1965Description : 1 vol. (VII-120 p.) ; 23 cmISBN : 9780521604826.ISSN : 0068-6824.Bibliographie : Bibliogr. p. 118-119. Index.Sujet MSC : 41A60, Approximations and expansions -- Approximations and expansions, Asymptotic approximations, asymptotic expansions (steepest descent, etc.)
41-01, Approximations and expansions, Instructional exposition (textbooks, tutorial papers, etc.)
En-ligne : Zentralblatt | MathSciNet
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Bibliogr. p. 118-119. Index

This monograph is an exposition of the most commonly employed methods for the determination of the asymptotic expansions of functions. These methods are amply illustrated by establishing asymptotic expansions for a number of special functions such as the gamma function, error function, Fresnel integrals, Bessel functions, the Legendre polynomials, and related functions. The chapter headings are: (1) Introduction, (2) Preliminaries, (3) Integration by Parts, (4) The Method of Stationary Phase, (5) The Method of Laplace, (6) Watson's Lemma, (7) The Method of Steepest Descents, (8) The Saddle-Point Method, (9) Airy's Integral, (10) Uniform Asymptotic Expansions. The emphasis throughout is on technique, especially in Chapters 7 and 8 where the subject matter is treated heuristically. The Laplace approximation in Chapter 5 is proved as is Watson's lemma in Chapter 6, this lemma providing a powerful tool for establishing the asymptotic expansions of functions representable as Laplace integrals. (MathSciNet)

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