The Lemniscate constant was news to me. You just gave me food to chew on further... The exploration continues... Thanks for the beautiful solution. I am elated when we get to the Gamma function and its sisters!
Whenever you see the square of Gamma Function of 1/4 in an integral, usually your answer will be a lot simpler if you express it in terms of either the Lemniscate Constant as you said, or with Gauss's Constant, G, the reciprocal of the arithmetic-geometric mean of one and the square root of two. If you multiply Gauss's Constant by Pi, you get the Lemniscate Constant. Using that constant. the value of the integral is: (G * Pi^2 ) / (2 * Sqrt[2] )
I think that once that the double integral has been reduced to a single integral, and the definition of sinhu=(e^u-e^-u)/2, take out a factor of e^u, and then expand the square root as a power series, and you end up integrating u^n*exp(-ax), and that gives you a nice series as a solution.
Lmao I've never heard of the beta, gamma, digamma functions, or the lmniscate constant. Still very much enjoyed the ride. Also, that's a psi, not a digamma, am I trippin?
I was solving PDE’s… you know… heat equation, waves equations, Laplace equation in any dimention and variation💪, but there is a problem with Poisson equation and Green’s function. I undrestand idea, but on wikipedia, the formula for Poisson equation has is not addicted to boundary and initial conditions… whatsmore i do not understand the notation… This is the last equation i wanted to study, but there is little information abput it… Anyway I am very addicted to mathematical analysis as you can see 😂, bu this is just beutiful when you solve all of this problems!!!
Hey..... Yeah I record in the late evenings and upload by midnight in my time zone.....I prefer replying quickly to the math chad society.....the bitches in the DMs can wait. Stay toxic😎
Why not improve handwriting coupled with verbal narration of elementary trigonometrical identity such as cosec^2. Also => implied by add confusion for motivated learners !
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This video is worthy of graduating to Maths 606. Just wow.
😂😂😂
Thanks mate
The Lemniscate constant was news to me. You just gave me food to chew on further... The exploration continues... Thanks for the beautiful solution. I am elated when we get to the Gamma function and its sisters!
Always a pleasure to watch your videos.
who the hell can expect this gorgeous result... that was breathtaking fr
Really good video, as always! Thank you for doing such cool things)
Thank you for this amazing effort.
✨👏Very nice solution ✨👏
❤️Thanks for again choosing my problem ❤️
That really was AMAZING. I started to see the Γ(1/4), (I shouted LEMNISCATE) then square root of two, and, then, PI. 😍
It's a beautiful result indeed
Excellent.
Your videos always make my day better.
Whenever you see the square of Gamma Function of 1/4 in an integral, usually your answer will be a lot simpler if you express it in terms of either the Lemniscate Constant as you said, or with Gauss's Constant, G, the reciprocal of the arithmetic-geometric mean of one and the square root of two. If you multiply Gauss's Constant by Pi, you get the Lemniscate Constant. Using that constant. the value of the integral is:
(G * Pi^2 ) / (2 * Sqrt[2] )
Feynman tech, beta to gamma, digamma antics? What's not to love? How do you spell the name of the constant at the end?
Lemniscate constant
Everybody gangsta until this guy starts using the gamma function
This integral was so interesting. Thank you.
I would have been fascinated to learn how such an integral arises in the first place.
My toxic trait is I can probably solve it but halfway through I'll be like "f this Im not doing all these calculations" and give up, don't solve it 💀
what you mean by toxic ??
I think that once that the double integral has been reduced to a single integral, and the definition of sinhu=(e^u-e^-u)/2, take out a factor of e^u, and then expand the square root as a power series, and you end up integrating u^n*exp(-ax), and that gives you a nice series as a solution.
Nice! Can you please give more details about this constant or alink to read about it.
A quick google search will reveal alot....
One can even try chatgpt (gonna do that now 😂)
Lemniscate constant
Yes,i found it on wikipedia,very interesting.thanks!
There is a paper on the proof of the lemniscate formulas and it's construction by Arseniy V. Akopyan.
does anyone know that pi and lemniscate constant ϖ are brothers
Going from x=yu to dx=y du just by adding the ds was clean😎😎
Lmao I've never heard of the beta, gamma, digamma functions, or the lmniscate constant. Still very much enjoyed the ride. Also, that's a psi, not a digamma, am I trippin?
It is psi but it's called digamma function
Aidez moi svp avec le nom du logiciel utilisé
Samsung notes
Maths505 merch when!?
I haven't mentioned anything about merch yet and I haven't exactly thought of it yet....perhaps sometime in the future
Finally Lemniscate constant!!!!!!
Bro how are you?
Haven't heard from you in so long....
I was solving PDE’s… you know… heat equation, waves equations, Laplace equation in any dimention and variation💪, but there is a problem with Poisson equation and Green’s function. I undrestand idea, but on wikipedia, the formula for Poisson equation has is not addicted to boundary and initial conditions… whatsmore i do not understand the notation… This is the last equation i wanted to study, but there is little information abput it…
Anyway I am very addicted to mathematical analysis as you can see 😂, bu this is just beutiful when you solve all of this problems!!!
@@nightmareintegral5593 look up Lawrence's text on PDEs....that'll help wonderfully
@@maths_505 Is this is that:
math24.files.wordpress.com/2013/02/partial-differential-equations-by-evans.pdf
?
bro do u even sleep
all videos are kept uploaded in midnight by you bruh
also u reply back to the comments in that time bro
Hey.....
Yeah I record in the late evenings and upload by midnight in my time zone.....I prefer replying quickly to the math chad society.....the bitches in the DMs can wait.
Stay toxic😎
Ur math is maulfunctioning to put cold fusion into an object
Gli integrali doppi ah ah..era un problema anche quando avevo 20 anni
sinch
Why not improve handwriting coupled with verbal narration of elementary trigonometrical identity such as cosec^2. Also => implied by add confusion for motivated learners !
d/dz (csc(π z)) = - π cot(π z) csc(π z)
Your pronunciation of sinh bothers me more than it should.