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.
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.
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
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!
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.
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
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 RUclips....no doubt😂😂
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 .
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😭
Very nice integral. Thank you
I am the first one to look out this cool integral with my eyes😢
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!
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?
@@uvtears 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
Not very satisfied with Li2(-2) ,what is it exactly ?
ln(27/4)-3+INT(ln(2+z)/(1+z)..z=0...1)
Hey bro do you have any book? I'd like to know if you have written a math book
Solve schrodinger equation
😭
[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