The I use this thread for giving the general formula for a superfunction \( \sigma \) of \( f \):
\( \sigma(x+1)=f(\sigma(x)) \)
\( \sigma'(x+1)=f'(\sigma(x))\sigma'(x) \)
\( \sigma'(x+n) = \sigma'(x)\prod_{k=0}^{n-1} f'(\sigma(x+k)) \)
\( \sigma(x+1)=f(\sigma(x)) \)
\( \sigma'(x+1)=f'(\sigma(x))\sigma'(x) \)
\( \sigma'(x+n) = \sigma'(x)\prod_{k=0}^{n-1} f'(\sigma(x+k)) \)
