for some reason i can never resist the urge to combine a difference or sum of sin(x) and cos(x) into a singular trig function so the final result can be rewritten as -cos(π/4 + 1) / [√2 sin(1)]
Random request I know, and you don't have to take it, but recently I've been hooked on geometric algebra. Built upon it is something called geometric calculus. Would you be willing to look into some problems from differential geometry and that sort of thing? :D
Michael Penn definitely solved the first sum a while back, but he only alluded to the second one also being cool, so it's cool to actually see the result. I do have to question the plugging in of j*a into the series, because the way I got to the original result for that series is with a fourier series expansion of e^ax and Parseval's identity, which needs a to be a real number
Hi, Amazing, not that common to get trigonometric lines of integers as result of series. "ok, cool" : 0:10 , 0:59 , 2:57 , 3:42 , 9:53 , 11:29 , "sorry about that" : 4:30 , "terribly sorry about that" : 8:27 , 10:03 .
Integers? Exquisite!
You make math so much fun, these results are mind blowing
for some reason i can never resist the urge to combine a difference or sum of sin(x) and cos(x) into a singular trig function so the final result can be rewritten as -cos(π/4 + 1) / [√2 sin(1)]
Very cool proof. Solution is innovative. Thanks.
sin(1) and cos(1) are cursed numbers, actually
Loved your "okayy, cool"
michael penn has covered those on his channel, i believe
The general case was discovered on my channel using the functional relationship between the gamma and zeta functions 😎
This is cool and good. :)
Of course, applying the switch up depends on convergence, but you're fine here. It's not super hard to prove convergence.
yo cool idea for an integral where i find but can't solve, so u have the triple integral where 0
Hey for your next video you should integrate sin(pi x)x^x(1-x)^(1-x) from 0 to 1
really cool 🤩🤩 i propose for the next video a contour integration 😋
Contour integration it is!
Random request I know, and you don't have to take it, but recently I've been hooked on geometric algebra. Built upon it is something called geometric calculus. Would you be willing to look into some problems from differential geometry and that sort of thing? :D
Michael Penn definitely solved the first sum a while back, but he only alluded to the second one also being cool, so it's cool to actually see the result.
I do have to question the plugging in of j*a into the series, because the way I got to the original result for that series is with a fourier series expansion of e^ax and Parseval's identity, which needs a to be a real number
@@Sugarman96 I used complex analysis to derive the series so I felt no hesitation in plugging in i*a 😂
The thing I really like about math UA-cam is seeing how different people, with differing skills and experience tackle the same problem.
You can also derive that infinite series for cot/coth by taking the logarithmic derivative of the sine infinite product, which is pretty cool I guess
Good work and Great video
link to the sum of 1/(n^2 + a^2) video?
Can you do a video about Cauchy's integral
i don't know the above one of an equation how to get the 1/(n2+a20) equal to the - 1/2a …..
In what classes would you learn some of the tricks like you used in this video?
@@thegermanempire9015 mostly being street smart 😂
Hi,
Amazing, not that common to get trigonometric lines of integers as result of series.
"ok, cool" : 0:10 , 0:59 , 2:57 , 3:42 , 9:53 , 11:29 ,
"sorry about that" : 4:30 ,
"terribly sorry about that" : 8:27 , 10:03 .
Yeah it's a pretty unconventional result
Its taking me so long to learn melodical whistling
Fantastic
How do you make your videos, I mean what gears do you use ?
No gear bro these videos are 100 percent natty
If you mean software then it's Samsung notes
Infinite series? I hardly know her
Explain
@@agrajyadav2951 Yes.