If we define a finite difference operator as [tex]\Delta a_n = a_{n+1}-a_n[/tex](adsbygoogle = window.adsbygoogle || []).push({});

Can we prove or disprove the existence of a function F, [tex]F:\mathbb{Z}\rightarrow\mathbb{Z}[/tex], such that [tex]\Delta F(g_n)=\frac{\Delta g_n}{ g_n}[/tex], where g is some arbitrary function?

Edit: fixed Big typo

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# Does there exist a function such that

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