An easy proof of Euler's Reflection formula

An easy proof of Euler's Reflection formula
Gamma(n)*Gamma(1-n) is equal to pi/sin(pi*z)
Integral x^m-1/1+x^n from 0 to infinity

[@mathematicsmi]

In the previous solution of the integral I used reflection formula. The method is still correct when we solve the integral by using complex analysis. Small error , and sorry 😢.

[@jhonvergara6891]

You are correct, but complex analysis is not necessarily used, the last integral can be calculated by series and it comes out simple

[@jhonvergara6891]

There is a detail in that proof you supply, because the integral you have left at the end uses what you are proving, the proper proof is to use series to prove the last integral, only true integral makers will know what I am saying.

[@PRAJWALKANDEL-xe6eo]

yes

[@dr.rahulgupta7573]

Thanks for presenting a nice identity in a simple manner.

[@mathematicsmi]

Thanks for watching and commenting to my videos. ❤️

[@MuhammadYogavas]

Hola Informàtic 23'
We didnt get the Beta function yet, but we need to solve this problem, is it possible ?

[@yoav613]

Nice but there is alittle problem since in your video when you solve the integral at the end you used euler reflection formula to solve it.. the way that euler reflection formula prooved in the books is by contur integration

[@mathematicsmi]

Yes you’re correct, actually I forgot that I used reflection formula when I solving the integral. Yes the way is complex analysis.

[@yoav613]

@@mathematicsmi any way it was nice.i learn alot from you and i like that you answer my comments and if there is any problem you tell me.you are very nice and kind

[@mathematicsmi]

@@yoav613 Thank you. You too nice, intelligence, and kind person.

[@user-wu8yq1rb9t]

Hello Dear *MMI*
Proof .... You should do it more.
Great
Thank you

[@mathematicsmi]

Welcome ❤️