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Asymptotic expansions

Copson, E. T. (1901-1980.)

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Asymptotic expansions

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Asymptotic expansions/ by E.T. Copson.
作者:	Copson, E. T.
出版者:	Cambridge :Cambridge University Press, : 1965.,
面頁冊數:	120 p. :ill., digital ;24 cm.
附註:	Title from publisher's bibliographic system (viewed on 05 Oct 2015).
內容註:	Introduction -- Preliminaries -- Integration by parts -- The method of stationary phase -- The method of Laplace -- Watson's lemma -- The method of steepest descents -- The saddle-point method -- Airy's integral -- Uniform asymptotic expansions.
標題:	Asymptotic expansions. -
電子資源:	https://doi.org/10.1017/CBO9780511526121
ISBN:	9780511526121

Asymptotic expansions
Copson, E. T.1901-1980.

Asymptotic expansions[electronic resource] /by E.T. Copson. - Cambridge :Cambridge University Press,1965. - 120 p. :ill., digital ;24 cm. - Cambridge tracts in mathematics ;55. - Cambridge tracts in mathematics ;55..

Title from publisher's bibliographic system (viewed on 05 Oct 2015).

Introduction -- Preliminaries -- Integration by parts -- The method of stationary phase -- The method of Laplace -- Watson's lemma -- The method of steepest descents -- The saddle-point method -- Airy's integral -- Uniform asymptotic expansions.

Certain functions, capable of expansion only as a divergent series, may nevertheless be calculated with great accuracy by taking the sum of a suitable number of terms. The theory of such asymptotic expansions is of great importance in many branches of pure and applied mathematics and in theoretical physics. Solutions of ordinary differential equations are frequently obtained in the form of a definite integral or contour integral, and this tract is concerned with the asymptotic representation of a function of a real or complex variable defined in this way. After a preliminary account of the properties of asymptotic series, the standard methods of deriving the asymptotic expansion of an integral are explained in detail and illustrated by the expansions of various special functions. These methods include integration by parts, Laplace's approximation, Watson's lemma on Laplace transforms, the method of steepest descents, and the saddle-point method. The last two chapters deal with Airy's integral and uniform asymptotic expansions.

ISBN: 9780511526121Subjects--Topical Terms:

526123
Asymptotic expansions.

LC Class. No.: QA312 / .C58 1965

Dewey Class. No.: 515.35

Asymptotic expansions
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520 $a Certain functions, capable of expansion only as a divergent series, may nevertheless be calculated with great accuracy by taking the sum of a suitable number of terms. The theory of such asymptotic expansions is of great importance in many branches of pure and applied mathematics and in theoretical physics. Solutions of ordinary differential equations are frequently obtained in the form of a definite integral or contour integral, and this tract is concerned with the asymptotic representation of a function of a real or complex variable defined in this way. After a preliminary account of the properties of asymptotic series, the standard methods of deriving the asymptotic expansion of an integral are explained in detail and illustrated by the expansions of various special functions. These methods include integration by parts, Laplace's approximation, Watson's lemma on Laplace transforms, the method of steepest descents, and the saddle-point method. The last two chapters deal with Airy's integral and uniform asymptotic expansions.
650 0 $a Asymptotic expansions. $3 526123
650 0 $a Integrals. $3 546791
830 0 $a Cambridge tracts in mathematics ; $v 55. $3 3470585
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