one of few integrals from your videos i actually was able to solve myself, but instead of using dilogarithm integral representation at the beginning, i expanded ln(1+e^(y-x)) into series and after integrating each term collected them into terms with eta function and two polylogarithms, really cool one!
sir can you please make an other video about contour integration but this time solving integrals involving the arctan function because i can't really understand the branch cuts in this type of integral i am waitinig for your answer best teacher ever 🥰🥰
Pollywog function? Does it display amphibious behavior and wiggle like a pollywog? Does it traverse the complex plane by hopping like a toad? You still spelled PolyLog wrong, bro.
I like seeing someone else devote a lot of time to considering which letter to make the substitution. Normally I don't use μ, λ or L in case they're mistaken as some kind of Lebesgue measure thing.
Yo what are those strange symbols?? I see them on my keyboard as I'm typing and it feels like I remember them from a past life but....what do they mean???
The sign error after the first integral is resolved is cancelled by the sign error with the dilogarithm expansion.
Yeah I noticed that while editing but honestly I thought it was so damn funny I left it in as a sort of easter egg 😂😂
Thats actually hilarious and amazing
Yo dawg i heard you liked cancelling signs so i made you a sign error that would cancel the sign error
Hi,
"ok, cool" : 4:29 , 6:30 , 7:30 , 10:25 , 11:51 , 13:56 , 17:44 ,
"terribly sorry about that" : 4:40 , 8:42 , 9:52 , 12:58 .
ok, cool
one of few integrals from your videos i actually was able to solve myself, but instead of using dilogarithm integral representation at the beginning, i expanded ln(1+e^(y-x)) into series and after integrating each term collected them into terms with eta function and two polylogarithms, really cool one!
Problem with the series expansions for the polylogs here is that they don't converge.
Thank you for this innovative solution.
Wow, I never heard you say “fuck” before
👏✨Well done !!✨👏 And ❤️Thanks! ❤️ for sharing
I believe it’s the Inversion formula for the Trilogarithm
sir can you please make an other video about contour integration but this time solving integrals involving the arctan function because i can't really understand the branch cuts in this type of integral i am waitinig for your answer best teacher ever 🥰🥰
Aight, lemme find some
Mathematica quickly gets -(1/2)+PolyLog[3,-(1/E)]+PolyLog[3,-E]+(3 Zeta[3])/2, where PolyLog[k,z] gives the PolyLog function Li_k (z)
Pollywog function? Does it display amphibious behavior and wiggle like a pollywog? Does it traverse the complex plane by hopping like a toad?
You still spelled PolyLog wrong, bro.
@@xleph2525 Autocorrect!!
@@xleph2525 lol
I kept expecting you to use the symmetry of the integral for something.
"OK Cool" should be your nickname
I like seeing someone else devote a lot of time to considering which letter to make the substitution. Normally I don't use μ, λ or L in case they're mistaken as some kind of Lebesgue measure thing.
congrats on the ladies view increase 🤣
19:16 can you make a video where we can see from where 1/3 comes from?, thats the part where I got lost, plis 🙏
I'm afraid I'm not qualified enough yet😭
Can you make a crash course about calcalus for people who havent the basics to follow you
What do you use to write everything?
At 3:03 shouldn't I= -½ MINUS the double integral?
A me risulta I=-1/2+(3/2)ζ(3)+2Σ((-1)^k)coshk/k^3...ma la serie non converge,boh
double trouble integral 😂😂
Didn’t you do this one but It goes to infinity instead of 1 ?
Nope...not with infinity.
Can you pls teach the polylogarithm reflection formula derivation? 😂
Interesting integral with solution that includes a coefficient of 4,5 when
Yo what are those strange symbols?? I see them on my keyboard as I'm typing and it feels like I remember them from a past life but....what do they mean???
19:16 :)
28th
I'll be a lady every other Thursday if that helps.
second
Third
Why 4 and a half ladies? What is a half lady?
Half a lady is a lady cut in half?
That's the DiLady function evaluated at "Terribly sorry about that."
Works like a charm out on dates