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.

- The term contributes 1 on the diagonals.
- The terms sum to .
- The terms (with a -1 in the matrix) are nearly the series for . The term is is missing so subtract 1. The middle matrix element is twice the other even terms.

Putting this all together, we get

Jim Branson 2013-04-22