Let f: S → S where S =(0, ∞) be a twice differentiable function such that f(x+1)=x f(x). If g: S → R be defined as g(x)= log_e f(x), then the value…

Let $\displaystyle f: \mathrm{S} \rightarrow \mathrm{S}$ where $\displaystyle \mathrm{S}=(0, \infty)$ be a twice differentiable function such that $\displaystyle f(x+1)=x f(x)$. If $\displaystyle g: \mathrm{S} \rightarrow \mathbf{R}$ be defined as $\displaystyle g(x)=\log _{\mathrm{e}} f(x)$, then the value of $\displaystyle \left|g^{\prime \prime}(5)-g^{\prime \prime}(1)\right|$ is equal to :