Symmetry and Separation of Variables
by Willard Miller
Addison-Wesley, Reading, Massachusetts, 1977 (out
of print)
PDF files
Chapter 1. The Helmholtz Equation
Chapter 2. The Schrödinger and Heat Equations
Chapter 3. The Three-Variable Helmholtz and Laplace Equations
Chapter 5. The Hypergeometric Function and Its Generalizations
Appendix A. Lie Groups and Algebras
Appendix B. Basic Properties of Special Functions