Inspired by this post, I thought I would ask a similar question. The Reciprocal Fibonacci constant $\psi$ is the value the infinite sum of the reciprocals of the Fibonacci numbers converge to, i.e:
$$\psi = \sum_{n=1}^{\infty} \frac{1}{F_n}$$
Is there any known integral representation for $\psi$? Or just interesting integrals in general containing $\psi$?
*To clarify, integrals like
$$\int_0^\infty e^{-\frac{x}{\psi}} dx = \psi$$ are NOT interesting integrals.
