Solving Bessel's differential equation using Frobenius Method part 1 of 2

[@apsFoz09]

Thank you for post this, I understand this resolution now!

[@SparkHorror-r5c]

Is that your child in the background by chance? Fantastic video by the way!

[@kylitrixgames4980]

Bro that's so annoying that sound

[@jbergamp]

Bibliography? It would be very much appreciated Bytheway, which coefficient we solve for when we create the equation for the recurrence relation? Thanks

[@daniel_an]

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.

[@daniel_an]

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.

[@jakubsz4602]

Wow fantastic

[@hadikhoshmaramzadeh1538]

Nice thanks for the video❤🙏

[@kylitrixgames4980]

9:07 and on many more time stamps, what is that annoying sound?

[@daniel_an]

Sorry. It's my mechanical keyboard.

[@kylitrixgames4980]

@@daniel_an ohh I see, it's allright

[@rogeliopaulinojr.5867]

Great video! Very clear and concise. Can I ask, how do you film this?

[@daniel_an]

Thanks! I use power point, with a USB pen-tablet, recorded with OBS studio. I also use SAMSON GO-Mic for recording voice.

[@rogeliopaulinojr.5867]

Thanks! Amazing content. 😊

[@chornnysmathforuni.6402]

Hello teacher, this lesson, Does it have for undergraduate level ??

[@daniel_an]

Yes. I intend this video and the following one accessible to anyone who took Calculus 2 and currently taking differential equations.

[@Uchechiconfidence-i4h]

I can barely see it clearly sir

[@daniel_an]

You probably have the video on 360p resolution. Please figure out how to change it.