A couple of days ago one of my teachers mentioned (when discussing the completeness of spherical harmonics) that [tex]{1,x,x^2,x^3,...}[/tex] forms an overcomplete basis for (a certain class of) functions. This implies that a power series expansion of a function is not unique. And you can for instance write [tex]x[/tex] as a sum over higher powers of [tex]x^n[/tex].(adsbygoogle = window.adsbygoogle || []).push({});

I tried to find something on the internet about it, because it's seems really odd to me. But I didn't find anything. Has anyone of you made this observation and maybe seen a proof of it? (Or is it just nonsense?)

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# Nonuniqueness of power series expansion

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