Proof of Euler's Integral Formula (Gamma Function)
48.6 هزار بار بازدید -
6 سال پیش
-
(The integral at the start
(The integral at the start of the video should say e^(-x), not e^(-nx). Sorry! Also, apologies for the screen flickering that happens during the video.)
In this video, we'll use differentiation under the integral sign to derive the integral formula for the gamma function, also known as Euler's integral of the second kind. We'll start with a simple integral of the exponential function, then differentiate both sides.
Leibniz's Integral Rule/Differentiation Under the Integral Sign: https://en.wikipedia.org/wiki/Leibniz...
The Gamma Function: https://en.wikipedia.org/wiki/Gamma_f...
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Video URL: Proof of Euler's Integral Formula (Ga...
Channel URL: @learnmathsfree
In this video, we'll use differentiation under the integral sign to derive the integral formula for the gamma function, also known as Euler's integral of the second kind. We'll start with a simple integral of the exponential function, then differentiate both sides.
Leibniz's Integral Rule/Differentiation Under the Integral Sign: https://en.wikipedia.org/wiki/Leibniz...
The Gamma Function: https://en.wikipedia.org/wiki/Gamma_f...
Like us on Facebook: Facebook: learnmathsfree
Follow us on Twitter: Twitter: LearnMathsFree
Google+: https://plus.google.com/u/0/b/1170336...
Video URL: Proof of Euler's Integral Formula (Ga...
Channel URL: @learnmathsfree
6 سال پیش
در تاریخ 1397/10/16 منتشر شده
است.
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