Let,s suppose we have a function f(x) wich is not on [tex] L^{2} [/tex] space but that we choose a basis of orthononormal functions so the coefficients:(adsbygoogle = window.adsbygoogle || []).push({});

[tex] c_{n}=\int_{0}^{\infty}dxf(x)\phi_{n}(x) [/tex] are finite.

would be valid to expand the series into this basis in the form:

[tex] f(x)=\sum_{n=0}^{\infty}\phi_{n}(x) [/tex] of course the sum:

[tex] \sum_{n=0}^{\infty}|c_{n}|^{2} [/tex] would diverge

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# Series expansion

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