Bessel Functions and the Frobenius Method
This video is a continuation to my Intro to Frobenius Method lecture. It's part 4 of my 'Topics in ODEs' playlist. In this video, I discuss the types of solutions to an ODE solved by the Frobenius Method which depend on the nature of the roots to the indicial equation. I then solve Bessel's equation by the Frobenius method.
Questions? Ask me in the comments!
Errata: The second term in the second solution for the repeated roots in the Frobenius Method (starts at 3:15) should begin at n = 1, and not n = 0. Also, the ln(x)'s in the y2's of both the repeated roots and integer different roots should be ln|x-x0|. In many examples, x0 = 0 anyway, so we should be fine. They're small mistakes, so hopefully it shouldn't be too impactful.
Prereqs: The first 3 videos of this playlist: • Topics in Ordinary Differential Equations
Lecture Notes: https://drive.google.com/file/d/0B_ur...
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