Symmetry and separation of variables
This book is concerned with the relation between symmetries of a linear second-order partial differential equation of mathematical physics, the coordinate systems in which the equation admits solutions by the separation of variables, and the properties of the special functions that arise in this manner. Some modern group-theoretic twists in the separation of variables method that can be used to provide a foundation for much of special function theory are exhibited. It is shown explicitly that all special functions that arise by the separation of variables in the equations of mathematical physics can be studied by using group theory. Successive chapters deal with the Helmholtz equation, the Schroedinger and heat equations, the three-variable Helmholtz and Laplace equations, the wave equation, and the hypergeometric function and its generalizations. Appendixes deal with Lie groups and algebras, basic properties of special functions, and elliptic functions. 2 figures, 22 tables, 141 references. (RWR)
- OSTI ID:
- 5260230
- Resource Relation:
- Related Information: Encylopedia of Mathematics and Its Applications. Vol. 4
- Country of Publication:
- United States
- Language:
- English
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