Download Introduction to Asymptotics and Special Functions by F. W. J. Olver PDF

By F. W. J. Olver

creation to Asymptotics and unique features is a finished creation to 2 vital themes in classical research: asymptotics and precise services. The integrals of a true variable are mentioned, in addition to contour integrals and differential equations with ordinary and abnormal singularities. The Liouville-Green approximation can also be considered.

Comprised of 7 chapters, this quantity starts with an outline of the fundamental innovations and definitions of asymptotic research and distinctive services, by means of a dialogue on integrals of a true variable. Contour integrals are then tested, paying specific awareness to Laplace integrals with a posh parameter and Bessel features of huge argument and order. next chapters concentrate on differential equations having typical and abnormal singularities, with emphasis on Legendre services in addition to Bessel and confluent hypergeometric features. A bankruptcy dedicated to the Liouville-Green approximation tackles asymptotic houses with recognize to parameters and to the self reliant variable, eigenvalue difficulties, and theorems on singular quintessential equations.

This monograph is meant for college students wanting simply an introductory direction to asymptotics and unique functions.

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