Symmetry and separation of variables
著者
書誌事項
Symmetry and separation of variables
（Encyclopedia of mathematics and its applications / edited by G.-C. Rota, v. 4 . Section,
Cambridge University Press, 1984
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注記
Imprint from label on t.p. verso. Imprint on t.p.: Reading, Mass. : Addison-Wesley, Advanced Book Program, 1977
Publication taken over by Cambridge University Press in 1984 with a new copyright date
Bibliography: p. 275-280
Includes index
内容説明・目次
内容説明
Originally published in 1977, this volume is concerned with the relationship between symmetries of a linear second-order partial differential equation of mathematical physics, the coordinate systems in which the equation admits solutions via separation of variables, and the properties of the special functions that arise in this manner. Some group-theoretic twists in the ancient method of separation of variables that can be used to provide a foundation for much of special function theory are shown. In particular, it is shown explicitly that all special functions that arise via separation of variables in the equations of mathematical physics can be studied using group theory.
目次
- Editor's statement
- Section editor's statement
- Preface
- 1. The Helmholtz equation
- 2. The Schroedinger and heat equations
- 3. The three-variable Helmholtz and Laplace equations
- 4. The wave equation
- 5. The hypergeometric function and its generalizations
- Appendices
- References
- Index.
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