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Bessel Function of the 2nd Kind | 2nd solution of Bessel's Equation
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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:
Questions/requests? Let me know in the comments!
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:
Questions/requests? Let me know in the comments!
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