Asymptotic Expansions (Cambridge Tracts in Mathematics, Series Number 55) - Hardcover

Copson, E. T.

Hardcover

ISBN 10: 0521047218 ISBN 13: 9780521047210

Publisher: Cambridge University Press, 1965

Synopsis

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.

About this title

Book Description:

The theory of 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.

About this edition

• Publisher: Cambridge University Press
• Publication date: 1965
• ISBN 10: 0521047218
• ISBN 13: 9780521047210
• Binding: Hardcover
• Number of pages: 128