## Complete Functions

A set of Orthonormal Functions is termed complete in the Closed Interval if, for every piecewise Continuous Function in the interval, the minimum square error

(where denotes the Norm) converges to zero as becomes infinite. Symbolically, a set of functions is complete if

where is a Weighting Function and the above is a Lebesgue Integral.

Arfken, G. Completeness of Eigenfunctions.'' §9.4 in Mathematical Methods for Physicists, 3rd ed. Orlando, FL: Academic Press, pp. 523-538, 1985.