Integral ln gamma from 0 to 1

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In this neat video, I calculate the integral of ln of the gamma function from 0 to 1, which is equivalent to the integral in the thumbnail. Surprisingly, this is not as hard as one might think; you just need to use Euler's reflection formula and the integral of ln of sin, which I've done in a previous video. Enjoy!

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Had me thinking this was Flammable Maths...trickery! Great video :)

WhattheHectogon

*Euler has joined the chat*

*Euler has left the chat shamefully*

JaydentheMathGuy

Great solving procedure. The ½ ln(2.pi) gives the constant ln( sqrt(2pi)). So: integral 0 to 1 ln [Gamma(x)/sqrt(2pi)] dx = 1
The sqrt(pi) hints that it is connected to the Gaussian probability integral.

Galileosays

Just lovely! Solving the integral with reflection and get another integral that is best solved by reflection.

qschroed

Crazy! I can't imagine how you even think of these problems!

dhunt

4:30 _What happens is, this integral gets rectified, and... ha! it gets rekt_

When you are an mlg pro even in maths
*G E T R E K T S O N*

allaincumming

Hi Dr Peyam. I relly like your way in solving matv problems. The thing what bothers me is that the camera is so far away from the whiteboard.... and i cant see that good....

muratkaradag

بارك الله فيك يا دكتور پايام نتيجة جميلة

BabyXGlitz

I enjoy your videos a lot, Dr Peyam. I would love to learn if there is a closed form of arc length of tan(x). Utilizing the arc length formula we get int sqrt(sec^4(x) + 1) and even WolframAlpha cannot evaluate it. I mention it purely out of curiosity, it is not any kind of assignment. Please keep up the great work.

gtweak

You had integrated ln(sinx) from 0 to pi at the end of the video about the product of sines.. Yeah.. I am watching you 👀:-)

ahmadkalaoun

Nice solution I solved it with Legendre formula

michelkhoury

Hi
Can you help me in this integral
Int (e^x cosx )^1/2 dx

رسوليقدوتي-قط

Sir please give proof of Euler reflection formula..

vaibhavkhadse

Why does the photo show from -1 to 0, but the vídeo from does show from 0 to 1? Are the answers the same?

carviryzen

I understand why you were able to combine the integrals with ln(Γ(x)) and ln(Γ(u)), but really, isn’t u=1-x, and therefore they aren’t the same integral?

akivas

Holly shit is this awesome thx for showing

maximilianmueller

+C!!!! DUDE ITS YOU FAILED YOU EXAMMM XD its ok bro you did all that work.

JaydentheMathGuy

Are you thinner my heart whats happening

federicopagano

With elementary functions, the integral of Γ(x) really is impossible to calculate. Maybe with non-elementary ones.
You can expand the integral at 0 using but then crazy stuff will happen xD.

Rundas

There is integral from -1 to 0 on the thumbnail. And it turns out that the integral is taken from 0 to 1. CLICKBAIT -UNSUBSCRIBE 😒(I am kidding 🤗🤗)

IoT_

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