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Abstract

The aim of this book is to present and explain methods of obtaining asymptotic expansions of solutions of certain linear differential equations in the complex plane for large values of /z/. We shall consider classes of equation whose coefficients are either powers or, in certain cases, polynomials in z. Equations of these types arising in various physical applications, and in the spectral theory of linear differential operators, are given. The authors hope that this book will be of use to mathematicians, both pure and applied, theoretical physicists and engineers, whether established in their professions or just setting out on research. The techniques employed are entirely classical in nature, the mathematical prerequisite of the book being the theory of functions of a complex variable, methods for solution of linear differential equations and some familiarity with the elementary special functions. While mention is made of formal methods leading to the local asymptotic behaviour of solutions in a sector at infinity, this information is often of limited use in applications where we wish to relate the behaviour of a solution in a sector at infinity to the behaviour at the origin or in an adjoining sector. The main emphasis of the book is therefore on the deeper problem of global methods which will produce asymptotic expansions of solutions valid in a full neighbourhood of an irregular singular point at infinity.

Additional information

Authors: PARIS R B CEA, CENTRE D'ETUDES NUCLEAIRES DE CADARACHE (FRANCE) WOOD A D NATIONAL INSTITUTE FOR HIGHER EDUCATION, DUBLIN (IRELAND) , CEA, CENTRE D'ETUDES NUCLEAIRES DE CADARACHE (FRANCE);NATIONAL INSTITUTE FOR HIGHER EDUCATION, DUBLIN (IRELAND)
Bibliographic Reference: BOOK: 344 P., 1986, ISBN 0-582-99455-1 WRITE TO LONGMAN SCIENTIFIC & TECHNICAL, LONGMAN GROUP UK LIMITED, LONGMAN HOUSE, BURNT MILL, HARLOW, ESSEX CM20 2JE (UK), PRICE: UKL 19, (EUR 10648 EN).
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