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Beautiful presentation! Love it!

@BriTheMathGuy

3 жыл бұрын

Thank you so much!

@joshuasusanto6626

3 жыл бұрын

Wonderful! Simply wonderful! This I'm placing on my journal to sleep.

@adritobiswas1982

2 жыл бұрын

Yup

Outstanding. Sometimes I wonder who's more impressive: the student who solved the integral or the person who conjured it.

Arms getting bigger, so is the channel!

@BriTheMathGuy

3 жыл бұрын

😂😅

The echo is a little jarring but nonetheless still a beautiful solution to such an intimidating integral! Good stuff

@sujitdey1717

3 жыл бұрын

And i thought i was the one who felt something was different.

@BriTheMathGuy

3 жыл бұрын

Sorry about that! It should be fixed in the future.

@sujitdey1717

3 жыл бұрын

@@BriTheMathGuy no problem the math was great as always. Love you and your content. 💙.

That feeling when n factorial cancels

That's a very very beautiful way of solving a particularly intimidating integral, you just won a suscriber

@BriTheMathGuy

3 жыл бұрын

Thanks so much!

Watching these videos makes me realize that my hunger for scientific knowledge is still stronger and bigger than my fatigue after a full-time, warehouse-assistant working day.

@BriTheMathGuy

3 жыл бұрын

We all crave it! Thanks for watching after your tough day!

That was so insightful. I have never dealt with an integral like that, but now I am confident that if I ever see one, not to panic. Thank you! I really enjoyed this video.

@BriTheMathGuy

3 жыл бұрын

Wonderful!

Very nice presentation! To be absolutely rigorous though, it'd be nice to mention that each of the series converge for all positive x (ratio test) and that the sum and integral can be interchanged (e.g. tonelli's theorem)

Watched to the end, liked, saved to favorite math playlist, already subscribed, there isn't just anything left to do.

@shivam5105

3 жыл бұрын

Become a Putnam fellow

@BriTheMathGuy

3 жыл бұрын

Wow thank you so much!

@aashsyed1277

3 жыл бұрын

@@BriTheMathGuy me too!!!!!!!!!!!!

Phenomenal!! Your way of presenting a problem is mind-blowing. Discussing the possible methods in a step, how to start solving it, best approach ... Everything illustrates how good you are in math and throws light on the beauty of math

5:11 i think swapping the integral and the infinite sum there requires using the dominated convergence theorem(if we think about it rigorously), very good presentation overall

Your videos kick ass man, I want to make ones just like them! I love this fast paced but concise format

@BriTheMathGuy

3 жыл бұрын

Thanks so much! Best of luck!!

Subscribed!! Brilliant way of solving the integral as well as presenting it. Loved the video!

@BriTheMathGuy

3 жыл бұрын

Awesome, thank you!

Wow! What a great way with words! I love your channel.

@BriTheMathGuy

3 жыл бұрын

Thanks so much! Have a great day!

What a tremendous exposition! New subscriber! Thank you for your material! 🌹🔥

The format of black screen, the math in all the details and the clean process with all the steps makes these series of tutorial useful.

You really should become a math professor....

@BriTheMathGuy

3 жыл бұрын

Currently an instructor (no Phd)😅

@arnavsoni1701

3 жыл бұрын

@@BriTheMathGuy great!!!

4:15 When he said "we still have some exes lingering about' , I felt that

That was amazing👏👏 Congratulations

@BriTheMathGuy

3 жыл бұрын

Thanks so much!!

This was amazing; thank you so much for sharing!

@BriTheMathGuy

3 жыл бұрын

Glad you enjoyed it!

That is a suprisingly beautiful result! Thank you for covering this in a video. :D

@BriTheMathGuy

3 жыл бұрын

My pleasure!

You release that you're good at math when u start watching the contents in x2

By looking at that integral, I instantly understood that I would not be able to solve it if I try. *And I was not disappointed*

@BriTheMathGuy

2 жыл бұрын

😂

Beautiful problem, and very beautiful answer. Using the sum representation of the exponential function and the Gamma function… what a ride haha. Love your channel!!

@BriTheMathGuy

2 жыл бұрын

Many thanks!

2:18 My dirty brain just hears a curse word

Your videos are so fun to watch.😃

@BriTheMathGuy

3 жыл бұрын

Glad you like them!

i appreciate this hope that maths will be fun and famous like nothing before once

The way you explain, makes these intimidating integrals seem easier

@BriTheMathGuy

3 жыл бұрын

Glad you think so! Have a great day!

I like that you get into the math immediately

Your presentation of the solution always gets me. My best wishes to you and please please continue

@BriTheMathGuy

3 жыл бұрын

Thank you, I will!

Wow!! Absolutely marvelous!!

@BriTheMathGuy

3 жыл бұрын

Thank you! Cheers!

I really enjoy these videos! Can't wait to start taking higher level maths in uni

@BriTheMathGuy

3 жыл бұрын

I'm so glad!

Such a great video!

@BriTheMathGuy

3 жыл бұрын

Glad you liked it!!

Nice proof ! Now you just need to justify swapping the sum and the integral.. as it cannot always be done .

@santiago_moralesduarte

3 жыл бұрын

The sum converges to less than e^(u/2)

うおおおお　Bravo!! めっちゃくちゃわかりやすかったです!!!😍😍😍👍👍👍

@BriTheMathGuy

3 жыл бұрын

Thanks so much!

Great u make maths lucid

Such the one of the best teacher ever

I can explain this integral just one word. WOW

@BriTheMathGuy

3 жыл бұрын

🤯

The second power series (1 + x²/2² + ...) equals the the Bessel function of the first kind J_0 evaluated at ix, although I don't know how that would be helpful in this problem.

@angelmendez-rivera351

2 жыл бұрын

It would be helpful if you are familiar with the Bessel functions, since they satisfy many integral equations.

So good video !

@BriTheMathGuy

3 жыл бұрын

Thanks so much!

i have no clue what he is talking about but i still love it

Incredible explanation!

@BriTheMathGuy

3 жыл бұрын

Glad you think so!

Great video, thanks Bri. What program are you using for the text?

cool integral, great video:D

@BriTheMathGuy

2 жыл бұрын

Glad you liked it!

Beautiful. I am so proud of myself that I solved it on my own. Edit: Okay maybe I didn't solve it completely correct lol I messed up a 2^r and got the answer e instead of sqrt(e)........ that is fine right!?!?!

@Rzko

3 жыл бұрын

no

@nikhilnagaria2672

2 жыл бұрын

yes

@10-year-oldcalculus19

2 жыл бұрын

Yesn’t

@georgeryandev2103

2 жыл бұрын

Yes, making mistakes is good for the growth of math skills.

Very nice. Thanks.

@BriTheMathGuy

3 жыл бұрын

Most welcome!

Beautiful!

@BriTheMathGuy

3 жыл бұрын

Glad you enjoyed it!

The awkward moment when a solution is as pretty as the one presenting it.

this goes way beyond advanced level of that pesky JEE

@dfsfssdfsdfs3084

3 жыл бұрын

Really? I thought the advanced JEE was the hardest test

You say that to all of them.

That worked out so perfectly lmao

This video is sooooo Good ❤❤ from Ethiopia, Africa

bro pls make more videos on putnam integrals .They are really interesting. Thank you in advance

This is awesome

5:05 why can we do this ? Permute the sum and the integral? Is it because the sum is converging uniformly on [0,+infinity] ?

@BrollyyLSSJ

3 жыл бұрын

I'd say dominated convergence theorem, with something like exp(-u+u/2) = exp(-u/2) being the integrable dominant.

@Rzko

3 жыл бұрын

The integral of the sum is the sum of the integrals because the integral is a linear function. Then you just put out of the integral the terms that don't have 'u', which means they are constants.

@tueur2squall973

3 жыл бұрын

@@Rzko U can do this when Everything is finite , I mean when the sum is finite , but when It's a series (infinite sum) , you need more argument : you need to know if the sum is converging , how it's converging in order to switch the sum with the integral

@tueur2squall973

3 жыл бұрын

@@Rzko And yeah Thank you , I did understand the following steps

@Rzko

3 жыл бұрын

@@tueur2squall973 are you sure about that? An infinite sum is just the limit of a partial sum (idk if we say like that in english)

Incredible!

@BriTheMathGuy

3 жыл бұрын

Glad you thought so!

I lost track for the first few times but I'm glad I understood this in the end :)

@BriTheMathGuy

2 жыл бұрын

it's a tricky one! :) thanks for watching!

@deekshanaik2438

2 жыл бұрын

@@BriTheMathGuy yea your vids are quite interesting... Who knew a bio nerd like me would binge math questions some day... Thanks for ur efforts

Amazing!

@BriTheMathGuy

3 жыл бұрын

You are!

🤩, it was a crazy integral, it involved power series gamma u sub,I want more integrals like this

Nice, I was able to do this one! Really awesome integral

@BriTheMathGuy

3 жыл бұрын

Great job!

Use double factorials. These are useful.

Woah!!! Mind blown...

@BriTheMathGuy

3 жыл бұрын

🤯

Always awesome like you are :-)

@BriTheMathGuy

3 жыл бұрын

You're the best!

This is so good

@BriTheMathGuy

3 жыл бұрын

Glad you thought so!

I love watching *other* people do integrals :)

hmmmm.. that integral can simplify like ʃ (1-x*exp(-x^2))*BesselI(0,x) dx and BesselI(0,x) is modified Bessel Function of the First kind

That was quite an aesthetic one

For the first factor I did the following pulled out x, substituted u=-x^2/2 For the second factor i have got second order linear differential equation but not with constant coefficients xy''+y'-xy=0 Second factor will probably be Bessel function but when we get first factor Gamma function will be helpful

Is there a Taylor series expansion that expands to the factor of (n!)^2?

I hear so much stuff about the Putnam being ridiculously hard, but every step here was the most obvious thing to do given the current stage. Like it's not something you just scribble down in a hurry, but it's something I imagine most mathematically experienced people could do. Lovely presentation though

Incredible

@BriTheMathGuy

3 жыл бұрын

Glad you thought so!

That was so enjoyable

at 3:30 u had a chance to turn that sum into e^2x*sum(n=0,infinity,1/2^2n)

The second part can also be written as (x^n)^2 / ((2^n)^2 * (n!)^2) and we can take the entire term into square like (x^n / 2^n * n!) ^2 which we can write as ((x^n/2^n)/n!)^2 = ((x/2)^n /n!) ^2 so we can put it into e^x form like (e^(x/2))^2 which basically is e^x.

@violintegral

Жыл бұрын

You made a mistake. In general, given a sequence a_n, the sum of (a_n)^2 is not equal to (the sum of a_n)^2

Mathematics always blows up my mind

@BriTheMathGuy

3 жыл бұрын

🤯

You did a HARD putnum problem in 6 minutes! So impressed ! I think you are a genius !

@magicmulder

3 жыл бұрын

He explained the solution in 6 minutes. No telling how long it took him to find the solution.

@aashsyed1277

3 жыл бұрын

@@magicmulder no but at least he is a genius .........

@magicmulder

3 жыл бұрын

@@aashsyed1277 He is very good, but most math students could solve that one. Genius is rare. Very rare.

it's crazy how something that looks absolutely nasty like this can simplify down into √e at the end

that was pretty cool

@BriTheMathGuy

3 жыл бұрын

Glad you thought so!

Are there any other places where i could find an integral like this with two sums multiplied together in the integrand?

Simplified results are beauty gives extraterrestrial vibes.

Why do we always end up at gamma in these types of problems 😂,

@BriTheMathGuy

3 жыл бұрын

I don't know! 😂

Super!

@BriTheMathGuy

3 жыл бұрын

Thank you! Cheers!

Amazing.

@BriTheMathGuy

2 жыл бұрын

Thank you! Cheers!

Awesome

Intimidating ❤️

@BriTheMathGuy

3 жыл бұрын

😬

Does the second series converge on 0 to INF though? I can't really see it because I suck at evaluating them functional series.

@umylten4142

3 жыл бұрын

The second series absolutely converges. If I call U(n) = {x^(2n)}/{[2^(2n)]*(n!)^2}, then you have: U(n+1)/U(n) = {x^2}/{4(n+1)^2}, which converges to 0 as n -> infinity, for all x in (0, infinity). By the ratio test, that series converges.

This one was very beautiful

@BriTheMathGuy

3 жыл бұрын

Glad you thought so!

I like your videos very much. One tiny suggestion though- can you slow down your speed while explaining such problems. You go very fast, which is problematic to understand what you are saying. I mean, before even I understand the concept you told, you move to another concept.

Nice answer

@BriTheMathGuy

3 жыл бұрын

Glad you thought so!

1:21, you can't use the same summation variable for the two sums, 2nd one should be 'm', or whatever, but not 'n'.

@manateepink9100

3 жыл бұрын

Wrong, those aren't nested sums, it's a product of sums, meaning the variable names do not share the same scope and therefore cannot collide.

can you cancel the x, in the same quick step where you cancel the 2^n?? since one of the limits of integration is 0 you would have a 0/0 in x, I'm not sure if it is allowed to cancel out the x there

I got the first sum. But was clueless about what to do with (n!)^2... Subbing x^2/2=u was brilliant bruh

Satisfying Answer

@BriTheMathGuy

3 жыл бұрын

I think so too!

why echo?

@BriTheMathGuy

3 жыл бұрын

Sorry about that! It should be fixed in the future.

awesome

integradating

@BriTheMathGuy

3 жыл бұрын

😂

These vedios are really good but I want to a one on some mathematical concepts or theory.

@BriTheMathGuy

3 жыл бұрын

I'll do my best!

I liked this