Very nice ❤, keep going my friend ❤❤❤

@OscgrMaths

2 күн бұрын

@@ADDiOUMAARIR Thank you!

I'm so glad you turned the volume down slightly when the marker was squeaky. It's so nice, thanks :) And overall, it is a really nice video

Very nice indeed! Well worth the wait!!!

@OscgrMaths

Ай бұрын

Thanks so much! Glad you enjoyed.

I have encountered many proofs of this before, but struggled to grasp them fully. Your explanation has finally clarified it for me. It remains rigorous yet you have made it remarkably engaging. I truly appreciate your clear and enjoyable explanation. Thank you very much. -------- We know that |a+b| ≤ |a| + |b| Replacing b with -b, we get |a-b| ≤ |a| + |-b|, but |'b|=|b|, so |a-b| ≤ |a| + |b|. Rearranging: |a-b| - |b| ≤ |a|. [*] With the same argument, by replacing a with -a, we get |a-b| - |a| ≤ |b|. [**] Combining * and **, we get ||a|-|b|| ≤ |a-b| ----- Well, I am not good at complex analysis, but I think the answer for (why) at 22:12, is because otherwise the function will no longer be analytic, and then we cannot integrate. ---- Thanks again for this great video.

@OscgrMaths

Ай бұрын

@@user-cd9dd1mx4n Thanks for the comment!

Good job!

@OscgrMaths

Ай бұрын

@@DavidMFChapman Thank you!!

Awesome and rigorous Video as always! By the way I would like to make a suggestion about a future video you can consider making on the relationship between the zeta function and the dirichlet eta function OR on the analetic continuation of the zeta function and its contribution to the studying of primes and number theory(euler product formula for the zeta function)❤!

@OscgrMaths

Ай бұрын

Thanks so much! I'll definitely take a look at these thanks for the suggestion.

@Georgeclassified

Ай бұрын

@@OscgrMaths My pleasure😄

Nice

@OscgrMaths

Ай бұрын

@@dakcom-mk6mp Thanks!

Hello, great videos!!

@OscgrMaths

Ай бұрын

@@leofoxpro2841 Thank you!

13:44 is always going to be...negative :)

Flammablemaths clones are rampant

such a nice applications of contour integrations , btw may i know what book you use to learn this method

@OscgrMaths

Ай бұрын

To learn complex analysis and contour integration, Introduction To Complex Analysis by Priestley is a classic! Thanks for the comment.

@gregoriuswillson4153

Ай бұрын

@@OscgrMaths Thanks for the reply bro , i would love to try

hi sir i really enjoyed the video but i have a question concerning the branch cut: why the pole -1 (is a real number ) isn't branch cut i mean for example in the integral proposed by Math 505 int from 0 to inf cos(x))/(π^2 - 4x^2) the poles when are real he made a branch cut i hope that you understand what i mean

@OscgrMaths

Ай бұрын

@@user-jm6rm2xn3z I know what you mean - my branch cut was only positive real axis so since the pole was negative it's okay. I could have chosen imaginary which would have changed the contour but I find real easier normslly

You act as if the two horizontal line segments of the keyhole contour are on the real axis: they’re not.

@OscgrMaths

Ай бұрын

@@girianshiido Great question! Thats the why I parametrised with 0 and 2pi. Also, as epsilon reaches 0, they do approach the real axis given that the circle they are coming from essentially approaches a point at the origin. Hope that clarifies!

Your profile picture is really interesting. Is it an atom?

@OscgrMaths

Ай бұрын

I believe it is electron shells!

Why is x between 0 and 1?

@OscgrMaths

28 күн бұрын

@@christoffel840 Because 1-x and x have to be greater than 0 as inputs to the beta function. Hope that helps!

How to reach you? Could you share an email?

@OscgrMaths

Ай бұрын

@@skyblue4558 Sure, you can email me at dydoscar@hotmail.com