Bessel Functions of Half-Integer Order
In this video, I explain and derive the Bessel Functions of Half-Integer Order. I show that the expressions for the solutions to Bessel's ODE when the differential equation has a half-integer order involve sines and cosines.
The derivation in this video makes use of the rules of the Frobenius Method, particularly the rules pertaining to the solutions when the roots of the indicial equation differ by an integer. Also, I got a pop-filter plugin for Audacity, so I hope the sound is sufficiently good quality.
Questions? Ask in the comments!
Gamma Function Video: • The Gamma Function, its Properties, and Ap...
Bessel Functions and Frobenius Method: • Bessel Functions and the Frobenius Method
Prereqs: The first videos in this playlist: • Topics in Ordinary Differential Equations
Lecture Notes: https://drive.google.com/file/d/0B_ur...
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