I'm trying to approximate the sum $\sum_{\alpha=1}^{\mu} \Big(1-\frac{(\alpha(2 \mu-\alpha))^2 \gamma_1 \gamma_2}{2n^2 \mu^4}\Big)^{\frac{\lambda}{2}}$ with an integral $\int_{a}^{\infty}\exp\left(\lambda\Big(\frac{(-4 \alpha^2 \mu^2 +4 \alpha^3 \mu - \alpha^4) \gamma_1 \gamma_2}{4 n^2 \mu^4}\Big)\right)d \alpha$ with $a>0$ using Laplace method ($\alpha$ may be seen as a size of subset of species in a population size $\mu$, therefore the lower bound on summation is 1). Unfortunately, the assumptions for it are violated ($\alpha_0=\mu$ is a minimum point, and $\alpha_0= 2 \mu$ makes no sense; it also yields $f(\alpha_0)=0$).
I'd be grateful if anyone could help with this approximation.