The long time approximation from the asymptotic power series

Question

what is the long time approximation from the following the asymptotic series function? $$t^{3\alpha-2}\sum_{n=0}^\infty\sum_{m=0}^\infty\frac{(-it^{\alpha})^{n}}{Γ(n\alpha+2\alpha)}\frac{(it^{\alpha})^{m}}{Γ(m\alpha+\alpha)}$$ Thanks for your advice.