0}$ have been given in [@ericksonmaller05].\
Exponential functionals of Lévy processes describe the stationary distributions of generalized Ornstein-Uhlenbeck (GOU) processes. More detailed, if $\xi_t$ tends to $+\infty$ as $t\to\infty$ almost surely, then the law of $V$ defined in is the unique stationary distribution of the GOU process $$\label{GOUdef}
V_t=e^{-\xi_t} \left( \int_0^t e^{\xi_{s-}}d\eta_s +V_0  \right),\quad t\geq 0,$$ where $V_0$ is a starting random variable, independent of $(\xi,\eta)$, on the same probability space (cf. [@lindnermaller05 Thm. 2.1]). Due to their importance in applications and their complexity, exponential functionals have gained a lot of attention from various researchers over the last 25 years. See e.g. the survey [@bertoinyor] or the more recent research papers [@PardoPatieSavov; @PardoRiveroSchaik] for results on exponential functionals of the form $V=\int_0^\infty e^{-\xi_{s-}} \, ds$. Exponential functionals where $\eta$ is a Brownian motion plus drift have been treated for example in [@kuznetsovetal]. The case of general Lévy processes $\xi$ and $\eta$ has been studied e.g. in our previous papers [@BLexpfunc] and [@BLMranges]. Nevertheless, for several of the more concrete results in [@BLMranges], the setting was narrowed down to the case where $\xi$ is a Brownian motion plus drift and $\eta$ a subordinator.

Still, in general the distribution of exponential functionals 