Richmond’s formula #1: , where:
- with ,
- with .
Richmond’s formula #2: , where:
- with , and where ‘s are the same as in the Richmond’s formula #1.
- Following bounds are valid: .
Note that the exponential generating function satisfies the second order ODE: .
Source: T1269 = A.N.Richmond “Expansion for the exponential of a sum of matrices”; Int. Journal of Control (issue and year unknown).