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used only for functions based on gamma, not functions with some obscure relation to gamma

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Asympotics of $\int_0^{\infty} \left[ Q(m,x)\right]^d dx$

I'm interested in the asympotic behaviour (assuming an exact solution is intractable) of $$I(m,d)=\int_0^{\infty} \left[ Q(m,x)\right]^d dx$$ for fixed $d \in \mathbb{N}$ (in particular, for $d=3$) a …