A second-order Ordinary Differential Equation

where is a constant and is a known function called either the density or Weighting Function. The solutions (with appropriate boundary conditions) of are called Eigenvalues and the corresponding Eigenfunctions. The solutions of this equation satisfy important mathematical properties under appropriate boundary conditions (Arfken 1985).

**References**

Arfken, G. ``Sturm-Liouville Theory--Orthogonal Functions.'' Ch. 9 in
*Mathematical Methods for Physicists, 3rd ed.* Orlando, FL: Academic Press, pp. 497-538, 1985.

© 1996-9

1999-05-26