This is the write up for the 4th problem on the Midterm.

I began by plugging the Rodrigues Formula, equation 3.50, into Ylm(x), equation33.50, for Plm(x). This led to a more useful equation for Ylm(x). By typing this formula into mathematica, I found the Ylm(x) for l=3 and m=2. This is the same solution that Jackson found. Since the formula that I plugged into mathematica proved correct (it matched Jackson's answer), I then applied it to l=4, m=0,1,2,3,4. I placed the results into a table called the extension of Jackson's Table of Spherical Harmonics