I don't understand how he get $b- \sqrt2, -a, -b$....
and what is the periodic function?
2026-03-26 20:26:11.1774556771
Proof periodic equation
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A periodic function is a function such that there exist $p > 0$, such that for all $x\in \mathbf{R}, f(x+p) = f(x)$. Here, he is using $f(x+1) = \sqrt 2 f(x) - f(x-1)$ to compute $f(x+n)$ for $n$ integer and see what is happening. He shows that $f(x+4) = -f(x)$ and deduces $f(x+8) = - f(x+4) = f(x)$