I quickly looked at the document and I do not think you compute the matrix exponential.
It appears to be an identity. It just says that a matrix to some power can be expressed as an infinite sum. You can use the two interchangably in your calculations. For another explaination of matrix exponential,
S.O.O Math: Matrix ExponentialPerhaps I missunderstand your question. What kind of information were you going to get from the calculation and how did you want to use it?