Complete Functions
A set of Orthonormal Functions 
is termed complete in the Closed Interval 
if, forevery 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 iscomplete if
where
is a Weighting Function and the above is a Lebesgue Integral.See also Bessel's Inequality, Hilbert Space
References
Arfken, G. ``Completeness of Eigenfunctions.'' §9.4 in Mathematical Methods for Physicists, 3rd ed. Orlando, FL: Academic Press, pp. 523-538, 1985.
- Heine-Borel Theorem
- Heine Hypergeometric Series
- Heisenberg Group
- Heisenberg Space
- Held Group
- Helen of Geometers
- Helicoid
- Helix
- Helly Number
- Helly's Theorem
- Helmholtz Differential Equation
- Helmholtz Differential Equation--Bipolar Coordinates
- Helmholtz Differential Equation--Cartesian Coordinates
- Helmholtz Differential Equation--Circular Cylindrical Coordinates
- Helmholtz Differential Equation--Confocal Ellipsoidal Coordinates
- Helmholtz Differential Equation--Confocal Paraboloidal Coordinates
- Helmholtz Differential Equation--Conical Coordinates
- Helmholtz Differential Equation--Elliptic Cylindrical Coordinates
- Helmholtz Differential Equation--Oblate Spheroidal Coordinates
- Helmholtz Differential Equation--Parabolic Coordinates
- Helmholtz Differential Equation--Parabolic Cylindrical Coordinates
- Helmholtz Differential Equation Polar Coordinates
- Helmholtz Differential Equation--Prolate Spheroidal Coordinates
- Helmholtz Differential Equation--Spherical Coordinates
- Helmholtz Differential Equation--Spherical Surface