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).
See also Adjoint Operator, Self-Adjoint Operator
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 Eric W. Weisstein
1999-05-26