Yes... dilogarythm appeared, and leaving the original integral as a "fancy constant" plus another integral is the same as not-solving the original integral. I'm disappointed.
@@sergiokorochinsky49nah, the integral was solved alright, reducing it to well-known constants and a special function invocation. Maybe it wasn't the "nice" result you expected?
You should add a +1ln1 to the result to complete the stair, and if you’re really felling fancy today, you can even add -0ln0 and “define” it as its limit when x goes to 0
Will it also cover the incomplete Airy functions/Scorer's functions Gi(x) and Hi(x), or just the complete Airy functions Ai(x) and Bi(x)? I know Gi(x)+Hi(x)=Bi(x), but they're still kind of significant.
Good practice with these is to use the inversion formula of the Dilogarithm to write Li_2(-2) in terms of Li_2(-1/2) and other terms, but this is also fine!
Yo Kamaal!! Have you ever thought about using spherical or cylindrical coordinates in triple integrals in a vid? Would that make some integrals easier?
Haha, that was awesome! 🎉 I was afraid I maybe couldn't follow, but it turned out to be no problem (pausing the video here and there to catch up, because you are way too fast for my brain cells, haha). Until you unexpectedly and almost casually pulled out the dilogarithm and the Dirichlet Eta function. There you got me! (As a regular viewer of your channel, at least I happen to know that this stuff exists.) One small point: Maybe you could add an extra pair of parentheses around the integrand when there is a sum in the integral, so we can infer the extent of the integral better? This would help with better following all this mind-f*ck, haha. 😂
Really an awesome integral you solved. Your authority and articulations on solving these type of difficult problems is certainly extraordinary
I was about to comment that thid is probably the most straightforward integral you've solved, but then dilogarithms appeared.
Yes... dilogarythm appeared, and leaving the original integral as a "fancy constant" plus another integral is the same as not-solving the original integral. I'm disappointed.
@@sergiokorochinsky49nah, the integral was solved alright, reducing it to well-known constants and a special function invocation. Maybe it wasn't the "nice" result you expected?
You should add a +1ln1 to the result to complete the stair, and if you’re really felling fancy today, you can even add -0ln0 and “define” it as its limit when x goes to 0
OHHHHH DAMN I AM SO MAD RN FOR NOT THINKING ABOUT THAT😭
Video about Aery's differential equation when?
OHHHH I FORGOT ABOUT THAT ONE!
Thanks for the reminder homie
Will it also cover the incomplete Airy functions/Scorer's functions Gi(x) and Hi(x), or just the complete Airy functions Ai(x) and Bi(x)? I know Gi(x)+Hi(x)=Bi(x), but they're still kind of significant.
@@maths_505I love your honesty lol
Hi,
1:53 : maybe we know by heart that the antiderivative of ln x is x ln x - x 🙂
"terribly sorry about that" : 1:03 , 1:57 , 3:36 , 4:32 , 4:40 , 6:53 , 7:33 , 10:19 ,
"ok, cool" : 1:09 , 2:17 , 3:40 , 5:09 , 10:26 .
0:05 Threesome = Triple integral with exactly one log. 🤔✅
It's not even double meaning, it's direct meaning
💀☠️🌚
🤣🤣🤣🤣🤣
My subscribers are the best math people on TH-cam....no doubt😂😂
Good practice with these is to use the inversion formula of the Dilogarithm to write Li_2(-2) in terms of Li_2(-1/2) and other terms, but this is also fine!
Very nice integral. Thank you
How to deal with the fact that the di-logarithm converges for z in the unit circle and -2 clearly doesn’t belong in there?
@@shieldmytears but 2^2=4>1, so…
You can use an inversion formula for the dilogarithm
Li_2(-2) = -Li_2(-1/2)-pi^2/6-ln^2(2)/2
Analytical continuation goes brrrr... 😂
Using the integral form of dilog are easy to do this step.
@vascomanteigas9433 indeed
Bro, you’re so clever. How do you find/discover these problems? Is there a resource I can use to practice problems as challenging as these?
@@acpwnd2020 this is from the Romanian mathematical magazine. Problem by Ankush Kumar parcha
I am the first one to look out this cool integral with my eyes😢
Yo Kamaal!! Have you ever thought about using spherical or cylindrical coordinates in triple integrals in a vid? Would that make some integrals easier?
Haha, that was awesome! 🎉
I was afraid I maybe couldn't follow, but it turned out to be no problem (pausing the video here and there to catch up, because you are way too fast for my brain cells, haha).
Until you unexpectedly and almost casually pulled out the dilogarithm and the Dirichlet Eta function. There you got me! (As a regular viewer of your channel, at least I happen to know that this stuff exists.)
One small point: Maybe you could add an extra pair of parentheses around the integrand when there is a sum in the integral, so we can infer the extent of the integral better? This would help with better following all this mind-f*ck, haha. 😂
Pretty soon you're gonna be solving them from the thumbnail (still watch the video though so I can get views😭😭😭)
Not very satisfied with Li2(-2) ,what is it exactly ?
A certain real number, although you probably don't want to hear that. 😉 Counterquestion: What exactly is ln(3)? 🤔
Hey bro do you have any book? I'd like to know if you have written a math book
ln(27/4)-3+INT(ln(2+z)/(1+z)..z=0...1)
Solve schrodinger equation
😭
OK, cool
Terribly sorry about that
[Rammstein voice]
X
XY
XYZ
Xyz Summon ! 🎉
You should be terribly sorry about being terribly sorry for like a gazillion times in a single video
Ah yes ofcourse terribly sorry about that