Bibliography? It would be very much appreciated Bytheway, which coefficient we solve for when we create the equation for the recurrence relation? Thanks
Well, part 1 (where there is no singularity at x=0) can be found in any differential equations textbook. Part 2 (for the Bessel's function of the second kind), many textbooks just say Yν(x)=cosνπJν(x)−J−ν(x)sinνπ and move on. I found the solution in the form of Frobenius method in some Engineering textbook, but I don't remember which one. I just googled it. Sorry.
For the Bessel's function of the first kind, we solve for the case when Frobenius index is r=n, and it's fairly straightforward. You let a_0 be 1/(n! 2^n) and then solve a_i using the recurrence relation (where you'll find that a_i for odd i will be zero). For the Bessel's function of the second kind, there is a choice you have to make in the middle of the calculation, and it's non-trivial. That's why I had to follow some book to figure out what to do. But again, I don't remember which book it was. Sorry.
Is that your child in the background by chance? Fantastic video by the way!
Bro that's so annoying that sound
Thank you for post this, I understand this resolution now!
Wow fantastic
Nice thanks for the video❤🙏
Great video! Very clear and concise. Can I ask, how do you film this?
Thanks! I use power point, with a USB pen-tablet, recorded with OBS studio. I also use SAMSON GO-Mic for recording voice.
Thanks! Amazing content. 😊
Bibliography? It would be very much appreciated
Bytheway, which coefficient we solve for when we create the equation for the recurrence relation? Thanks
Well, part 1 (where there is no singularity at x=0) can be found in any differential equations textbook. Part 2 (for the Bessel's function of the second kind), many textbooks just say Yν(x)=cosνπJν(x)−J−ν(x)sinνπ and move on. I found the solution in the form of Frobenius method in some Engineering textbook, but I don't remember which one. I just googled it. Sorry.
For the Bessel's function of the first kind, we solve for the case when Frobenius index is r=n, and it's fairly straightforward. You let a_0 be 1/(n! 2^n) and then solve a_i using the recurrence relation (where you'll find that a_i for odd i will be zero). For the Bessel's function of the second kind, there is a choice you have to make in the middle of the calculation, and it's non-trivial. That's why I had to follow some book to figure out what to do. But again, I don't remember which book it was. Sorry.
Hello teacher, this lesson, Does it have for undergraduate level ??
Yes. I intend this video and the following one accessible to anyone who took Calculus 2 and currently taking differential equations.
9:07 and on many more time stamps, what is that annoying sound?
Sorry. It's my mechanical keyboard.
@@daniel_an ohh I see, it's allright
I can barely see it clearly sir
You probably have the video on 360p resolution. Please figure out how to change it.