Let $\Gamma(a,x) = \int_x^\infty t^{a-1} e^{-t} dt$ be the incomplete gamma function. What is the limit $$ \lim_{p \to \infty} \frac{1}{\sqrt{p}} \Big[\Gamma(p+\tfrac12,x)\Big]^{\frac{1}{2p}} $$ as a function of $x$?
2026-04-09 02:27:34.1775701654
Limit involving incomplete gamma function
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