We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.
We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.
Published online by Cambridge University Press: 05 March 2013
The aims of this book are twofold. The first is to present a detailed account of the classical method of steepest descents applied to the asymptotic evaluation of Laplace-type integrals containing a large parameter, and the second is to give a coherent account of the theory of Hadamard expansions. This latter topic, which has been developed during the past decade, extends the method of steepest descents and effectively ‘exactifies’ the procedure since, in theory, the Hadamard expansion of a Laplace or Laplace-type integral can produce unlimited accuracy.
Many texts deal with the method of steepest descents, some in more detail than others. The well-known books by Copson Asymptotic Expansions (1965), Olver Asymptotics and Special Functions (1997), Bleistein and Handelsman Asymptotic Expansion of Integrals (1975), Wong Asymptotic Approximations of Integrals (1989) and Bender and Orszag Advanced Mathematical Methods for Scientists and Engineers (1978) are all good examples. It is our aim in the first chapter to give a comprehensive account of the method of steepest descents accompanied by a set of illustrative examples of increasing complexity. We also consider the common causes of non-uniformity in the asymptotic expansions of Laplace-type integrals and conclude the first chapter with a discussion of the Stokes phenomenon and hyperasymptotics.
The next two chapters present the Hadamard expansion theory of Laplace and of Laplace-type integrals possessing saddle points. A study of these chapters makes it apparent how this theory builds upon and extends the method of steepest descents.
To save this book to your Kindle, first ensure [email protected] is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.
Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.
Find out more about the Kindle Personal Document Service.
To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Dropbox.
To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.
