A complete set of discrete eigenfunctions obeys the orthonormalization conditions Complementary to these is the set of closure relations For real eigenfunctions the complex conjugate can be dropped The finite sums for up to 100 are evaluated in this Demonstration Four systems are considered 1 infinite squarewell potential with and eigenfunctions ; 2 linear harmonic oscillator with and ; 3 linear rigid rotor for fixed ; 4 hydrogenlike radial function with For the first three cases the sum approaches an oscillatory representation of the delta function However the hydrogenic functions represent only the discrete bound states They do not constitute a complete set of eigenfunctions without including the continuum The sums usually exhibit erratic behavior but sometimes do show a peaking particularly for larger values of