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:
.
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Source: T1269 = A.N.Richmond “Expansion for the exponential of a sum of matrices”; Int. Journal of Control (issue and year unknown).