Special Functions & Their Applications

by Nikolai Nikolaevich Lebedev, Richard R. Silverman (Translation)

Famous Russian work covers basic theory of the more important special functions and their application to specific problems of physics and engineering. Most space devoted to the application of cylinder functions and spherical harmonics. Also explores gamma function, probability integral and related functions, Airy functions, hyper-geometric functions, more. Translated by Richard Silverman.

Genres: Mathematics, Reference, Physics

336 pages, Paperback

First published June 1, 1972

Reviews

[Tomáš Ševček · Rating 5 out of 5]

Although the syllabi of PDE courses for general mathematicians have changed drastically over the past 70 years, with the focus shifting from special functions to qualitative analysis and applications of functional analysis, this book is still an interesting read not only for engineers. The book covers some of the most widely used special functions (such as the gamma function, orthogonal polynomials, Bessel functions and many others), deriving some of their most useful properties and presenting problems in which they are employed. The book can definitely serve as a reference when one needs to look up the most commonly used properties of the functions. In order to follow the exposition, you should know your analysis (both complex & real) and ODEs very well. It also helps to be familiar with PDEs, since most of these functions actually arise when solving certain PDEs. I believe that this part is not stressed enough in the book. The book usually starts with definitions (usually as solutions to ODEs) of said functions and sometimes readers new to this area might keep wondering why one should be interested in solutions to certain wild-looking ODEs. It becomes clear only in the applications (when these specific ODEs arise when solving certain PDE problems on specific domains through the separation of variables). Therefore, I believe it might have been better to start with motivating examples first. Nevertheless, I highly recommend this book to anyone interested in special functions or in solving PDEs on specific domains.

[Nick Black]

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