수학:스털링_근사

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수학:스털링_근사 [2020/10/25 00:27] – [안장점 방법을 이용하는 유도] admin수학:스털링_근사 [2023/09/05 15:46] (current) – external edit 127.0.0.1
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 \[ \int_0^\infty e^{-p(z-\ln z)}dz \sim \sqrt{\frac{2\pi}{p}} e^{-p} \] \[ \int_0^\infty e^{-p(z-\ln z)}dz \sim \sqrt{\frac{2\pi}{p}} e^{-p} \]
 이고 따라서 이고 따라서
-\[ \Gamma(p+1) \sim p^{p+1} \sqrt{\frac{2\pi}{p}} e^{-p} = \sqrt{2\pi} p^{p+1/2} e^{-p}. \]+\[ \Gamma(p+1) \sim p^{p+1} \sqrt{\frac{2\pi}{p}} e^{-p} = p^p e^{-p} \sqrt{2\pi p}. \]
  
 +
 +======참고문헌======
 +  * https://www.math.unl.edu/~scohn1/8423/intasym1.pdf
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