Compute the Rotation Operator

All the odd powers are the same. All the nonzero even powers are the same.
The
s all cancel out.
We now must look at the sums for each term in the matrix and identify the function it
represents.
If we look at the sum for the upper left term of the matrix, we get a 1 times
. This is just
.
There is only one contribution to the middle term, that is a one from
.
The lower right term is like the upper left except the odd terms have a
minus sign.
We get
term n. This is just
.
The rest of the terms are zero.

Jim Branson 2013-04-22