Complete Biorthogonal System

A set of functions ${f_1(n,x),f_2(n,x)}$ is termed a complete biorthogonal system in the closed interval if, they are biorthogonal, i.e.,

			(1)
			(2)
			(3)
			(4)
			(5)

and complete.

A complete biorthogonal system has a very special type of generalized Fourier series. The prototypical example of a complete biorthogonal system is ${sin(nx),cos(nx)}_(n=0)^infty$ over , which can be used as a basis for constructing "the" Fourier series of an arbitrary function.

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Cite this as:

Weisstein, Eric W. "Complete Biorthogonal System." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/CompleteBiorthogonalSystem.html

Complete Biorthogonal System

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