Can someone be willing to show me the prove of why $\int_0^{\infty} u^{\alpha - 1} e^{-u}du = \tau(\alpha)$ is true. I'm confused as to why it is. I'm proving the Gamma Distribution pdf is equal to $1$, and I'm stuck here. I just want the comprehension and intuition behind it. Any help appreciated!
2026-04-08 04:45:34.1775623534
Understanding why $\int_0^{\infty} u^{\alpha - 1} e^{-u}du = \tau(\alpha)$
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