Linear combination of numbers: Express the $n^{th}$ Fibonacci number in terms of known constants.

Question

Given the concept that any number can be expressed as a combination of other numbers can the $n^{th}$ Fibonacci number be expressed in terms of $\zeta(3)$ and $\ln(2/e)$ ? If possible, show all work in the derivation. \begin{align} F_{n} = \sum_{r} \left[ a_{r} \zeta^{r}(3) + b_{r} \ln^{r}(2/e) \right] \end{align} where $a_{r} \neq 0$ and $b_{r} \neq 0$ are to be determined.