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Mathority
Добавлен 20 ноя 2023
A Real Result To An Imaginary Inquiry: iⁱ
This video examines a very mind-boggling result from Euler's formula. I hope you all enjoy :)
Просмотров: 437
Видео
Euler's Original Proof Of Basel Problem: Σ(1/n²)=π²/6 - BEST Explanation
Просмотров 13 тыс.6 месяцев назад
This video covers Leonhard Euler's original solution to the infamous Basel Problem! - This is also a re-upload since my previous version of the solution didn't adequately explain a certain crucial step, so I decided to remake the whole thing with a better explanation. I hope you all enjoy, and I greatly appreciate all of y'all's support! :)
A Simple Yet Interesting Differential Equation: dy/dx = x+y
Просмотров 123 тыс.7 месяцев назад
A quick and simple walkthrough of an interesting differential equation.
Where did the Gamma Function come from?!?! (Full Derivation)
Просмотров 24 тыс.7 месяцев назад
An intriguing and in-depth derivation of the notorious, yet spectacular, Gamma Function. Get some popcorn, this one's interesting!
An INCREDIBLE Factorial-tastic Infinite Sum of n!²/2n! (Wolfram Alpha can't explain!)
Просмотров 1,5 тыс.7 месяцев назад
An wonderful infinite sum with an equally spectacular solution, making use of various neat concepts such as Factorials, the Gamma Function, the Beta Function, Fubini's Theorem, a Geometric and Power Series, an interesting technique for Polynomial long division, Integration using Completing the Square, and Trig substitutions! If you are a fellow math enthusiast, you will be pleased :) Here's my ...
An Interesting Geometric-like Series
Просмотров 3368 месяцев назад
Evaluating a simple, yet interesting infinite sum.
Nice one,thanks
The first half of the video proving the Euler product formula for sine is just a basic overview for why the formula is consistent, but not a rigorous proof that it is equivalent to sin(x). The proof is much more advanced and involves integrals, and was only proven over 200 years after Euler proposed it
At 7:34 amongst all the sines and pi stuff, you introduced a tangent. Excellent!
@@bazsnell3178 haha true! Thanks so much for watching!
Great video dude
@@HugoBossFC appreciate it! Thanks so much for watching!
And so on and so forth...
I for the first time saw your channel It was wonderful and very clear explanation. Please keep on making videos.. Thanks for your efforts🙏🙏🙏🙏
@@sadececns00 thank you so much for the kind works! Really appreciate you watching the video! I will begin uploading again soon. Unfortunately, have been really busy with work lately, but I hope to make some great new videos as soon as possible! :)
I’m sorry, but this did *not* have to be 20 minutes long. Needlessly dragging this over
Wow, that was a cool video! Euler was a super genius
@@anad8341 he was! And thanks so much for watching, really appreciate it!
nice I was stumped thank you.
@@foxlies0106 thanks for watching!
Really like your presentation --- Thank you so much!
Incredible content. For someone whose primary math source is RUclips it is sometimes hard to find a video that I can understand this clearly without having to check others explanations. I also watched the gamma function video and it was "diáfano" as we could say in Spanish. I wonder if you'll treat the transcendence of Euler's number someday
Thank you so much for this awesome proof!
Great video! My question is, how to get to the expansion of this integral to non-integer numbers?
Excellent intuition , thank you ❤
Simple and elegant.
Hats off ! Brilliant explanation. How did the lower and upper bound of integration between 0 to 1 in the log function come about?
very good demostration!
🎉🎉🎉
May God bless you and receive you in Glory. This is incredible. Thank you so much!
Thanks so much for watching and for the kind words! God bless you too! 😄
@@Mathority1729 is there a community on discord or anything for your channel? Or if there is a way to get in touch with you at all?
thank you so much 🤩🤩🤩
Of course! Thank you for watching! 😄
x ln(x)=0 for x=1
Small problem dealing with limit at x=1
Thank you so much for this explanation, finally got it 😊
Thank you for providing the clear explanation of gamma function
No problem! Thank you so much for watching! 😄
This is the best derivation of gamma function on RUclips cause it starts with an observation I.e. reality, I mean math itself. Nearly all other derivations out there are just some “rigorous proofs” of a some formula brought from heavens of the Lord by a genius man already knowing the formula. Please do a similar work for Lambert W
Hahaha thanks a ton! I’m really glad you enjoyed the video! And I agree, it’s more fun and useful to derive concepts in a way that is more straightforward and realistic, especially for the average person! I think this is how you bring people into mathematics!
Great video! Easy to follow and to understand :) . But why does the gamma function work for all z element C, R(z) > 0?
Thanks a ton for watching! Appreciate it! That’ll have to be an entirely separate video haha
@@Mathority1729 can't wait to see it :)
i loved it tysm
So glad you enjoyed it! Thanks so much for watching! 😄
amazing derivation of GAMMA´s FUNCTION , well explained and very didactic
Thank you so much! Really appreciate you watching! Glad you enjoyed 😃
best proof i have seen on youtube for the gamma function thanks alot for this amazing video
Thanks so much for the kind words, really glad you enjoyed the video!! 😄
Oh god thanks
No problem, thanks a ton for watching! :)
I am having trouble making intuitive sense of this from 4:40 onwards. question 1 : when x->0, (sin x)/x evaluates to 1. And on the right side you are putting x as zero. wouldn't that mean dividing the left hand side by 0 which is not allowed? maybe I am confusing the basic calculus here. question 2 : after this step, you are arriving at a value of k. But this is a value of k evaluated at x->0. How can we use this value of k in the main formula and say that is the value of k for "all values of x"?
lim at zero of a function that can be evaluated at 0 is just the value of that function at zero. k is a constant so if k at zero is a value, its always that value
3:22 A circular reasoning! How do we know that sin differentiates to cos?
Draw a simple right angle triangle. U ll get it.
@@sujitmohanty1try to work out the derivative of sin using the limit definition
How can you divide both sides of x if x may equal 0?
@@Larbitoso_o you’re correct, but only when he computes the limit of sin(x)/x. That had nothing to do with his next step of dividing both sides by x
Thanks for showing everything step-by-step and not skipping any parts. This was really fascinating to see, I always wondered how a factorial of a non-integer could be computed and the gamma function formula you derived shows how we can find the result. I'm excited for more of your videos! Edit: What side are you on, do you agree with the formula having n+1 within its parameters or just n.
This summation only holds truth if -1<x<1 right?
Yes otherwise the summation would diverge
Beautiful ❤️❤️
Thanks so much :)
Origin of lambert W function please
Wonderful video
Thank you so much! 😄
One reason for the shift might be because the gamma function becomes the mellin transform applied to e^(-u).
You earned my subscription, the video was clearly explained
Thanks a ton! Glad to hear you enjoyed it! 😄
Why, when differentiating 'the solution' do we not get back the original equation...as a proof, so to speak? Just subscribed in the hope of an explanation?
Interesting proof of n!
I appreciate that, glad you enjoyed! Thanks for watching 😄
Thank you so much... really helpful
Glad you enjoyed! Thanks for watching! 😄
This was both detailed and clear, a real matter class in how to explain complex ideas
I really appreciate that! Glad you enjoyed! Thank you so much for watching and for the kind words 😄
What program do you write on?
Another derivation, the Laplace Transform of a polynomial function yields the result when evaluated at s=1.
Absolutely, that’s another great way! Thanks for watching, rly appreciate it 😄
dy = x + y __ dx assuming y=Ax^2+Bx+C easily can be demostrated that A=0, B=C, B+1=0, B=-1, C=-1 then: y=-x-1 done! checking: dy = -1 = x + y = x - x -1, which is correct __ dx I know is too simple... but why complicate things? 😄
Thank you❤
Of course! Thanks for watching! 😄
Please derive in the similar way a formula for Beta function.
Where does the intuition / reasoning for the variable substitution starting at 18:24 come from? That's the only thing I'm confused on. Like just why that particular set of substitutions??