Symmetry and Separation of Variables

This 1977 volume is concerned with the group-theoretic approach to special functions.

Willard Miller (Author)

9780521302241, Cambridge University Press

Hardback, published 28 December 1984

318 pages
25.4 x 17.8 x 1.9 cm, 0.77 kg

Review of the hardback: ' … an important step in the group-theoretic approach to special functions. It is clearly written and should be accessible to a broad spectrum of readers'. Mathematical Reviews

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.

Editor's statement
Section editor's statement
Preface
1. The Helmholtz equation
2. The Schrödinger 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.

Subject Areas: Calculus & mathematical analysis [PBK]