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In this video I will, in case #1, I will solve the differential equation for the theta function (zenith direction, y-z plane) when n=1,l=0, and m(l)=0. We have to substitute x=cos(theta) so that the new function f(x)=f(cos(theta))=ThetaFunction(theta). For the non-normalized solution we know that the solution for f(x)=1. For the normalized solution we need to normalize the function such that f(x)-f(cos(theta))=A.
Next video in this series can be seen at:
https://youtu.be/S0DdQtvdIp4