$$\int\_{0}^{\infty}\frac{x^{v-1}}{e^{-\beta\mu}{e^x}-1}=\Gamma(v)\left(e^{\beta\mu}+\frac{e^{2\beta\mu}}{2^v}+\frac{e^{3\beta\mu}}{3^v}+\dotsb\right)$$

This integral is given in my statistical physics assignment and I feel that the $\mu$ in the integrand should have the opposite sign (as my results would make more sense) but I don't know how to prove this and I can't find the formula anywhere. I would love to find a source for this formula.