# Solve the functional equation $f(x+1)-f(x)=x*\sin(x)$ [closed]

Solve $$f(x+1)-f(x)=x*\sin(x)$$

## closed as off-topic by ArsenBerk, Leucippus, YiFan, Sil, ShogunJun 9 at 21:28

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• What have you tried so far? – ArsenBerk Jun 9 at 19:46
• @ArsenBerk calculus of finite differences – MorrisonFJ Jun 9 at 19:48

Take any function $$f(x)$$ defined on $$[0,1)$$ and then continue to all $$x$$ using the equation.
• Bonus: If $f$ is continuous on $[0,1)$ and $\lim_{x\to1^-}f(x)=f(0)$, then the continuoation will be continuous on all of $\Bbb R$. – Hagen von Eitzen Jun 9 at 20:14
• @HagenvonEitzen but $f(x)=1/4 csc^2(1/2) (sin(x)-x (sin(1-x)+sin(x)))$ . I don't know how to come to this decision – MorrisonFJ Jun 9 at 20:17