If $f(x+1) + f(x-1) = \sqrt3f(x)$, then what is the period of $f(x)$?
periodicity of function
2
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analysis
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6And what have you tried? – 2011-05-07
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0Hint: Mathematica says that your $f(x)$ are of the form $f(x)=e^{-\frac{1}{6} i \pi x} \left(a+b e^{\frac{i \pi x}{3}}\right)$ for some real $a,b$ – 2011-05-07
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0@user3123 : Actually, I think Mathematica's answer is not exhaustive. You can take $a$ and $b$ to be any $1$-periodical function. – 2011-05-07
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0ok I did not check that – 2011-05-07