Uploaded July 2017 | Updated September 2026, 2 weeks ago
In this video, I briefly describe how to obtain the Bessel function of the second kind, which is also the 2nd solution to Bessel's equation when the order of the ODE is an integer. People requested this video in the past so I hope this video is sufficient!
Deriving Y_n is fairly simple: take a particular linear combination of J_p and J_-p, and then let p approach n. I don't go through the entire calculation, because it's tedious and doesn't really teach much, but I refer you to this document (by Jim Lambers at Berkeley) if you're interested in the details:
https://math.berkeley.edu/~linlin/121B/LambersBessel.pdf
Questions/requests? Let me know in the comments!
Prereqs: The first 8 videos of this playlist: youtube.com/playlist?list=PLdgVBOaXkb9ATVsK2Q84ghjBgIk5faHNc
Lecture Notes: drive.google.com/file/d/0BzC45hep01Q4UlV4STFrN2FkS28/view?usp=sharing&resourcekey=0-vqJpghWmz_LeSXLII3Pp3Q
Patreon: patreon.com/user?u=4354534
Twitter: twitter.com/FacultyOfKhan
In this video, I briefly describe how to obtain the Bessel function of the second kind, which is also the 2nd solution to Bessel's equation when the order of the ODE is an integer. People requested this video in the past so I hope this video is sufficient!
Deriving Y_n is fairly simple: take a particular linear combination of J_p and J_-p, and then let p approach n. I don't go through the entire calculation, because it's tedious and doesn't really teach much, but I refer you to this document (by Jim Lambers at Berkeley) if you're interested in the details:
https://math.berkeley.edu/~linlin/121B/LambersBessel.pdf
Questions/requests? Let me know in the comments!
Prereqs: The first 8 videos of this playlist: youtube.com/playlist?list=PLdgVBOaXkb9ATVsK2Q84ghjBgIk5faHNc
Lecture Notes: drive.google.com/file/d/0BzC45hep01Q4UlV4STFrN2FkS28/view?usp=sharing&resourcekey=0-vqJpghWmz_LeSXLII3Pp3Q
Patreon: patreon.com/user?u=4354534
Twitter: twitter.com/FacultyOfKhan
