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- roots α, β
- 1/(z^2 + bz + 1) = A/(z - α) + B/(z - β)
- 1/(z^2 + bz + 1)^m = sum (m choose k) [A/(z - α)]^k + [B/(z - β)]^(m-k)
- residual of z^(m-1)/(z^2 + bz + 1)^m at α
- =
- coefficient of 1/(z - α) in z^(m-1)/(z^2 + bz + 1)^m
- =
- sum (m choose k) (coefficient of 1/(z - α) in z^(m-1) ([A/(z - α)]^k + [B/(z - β)]^(m-k)))
- ={ k has to be 1 }=
- (m choose 1) (coefficient of 1/(z - α) in z^(m-1) ([A/(z - α)]^1 + 0))
- =
- m z^(m-1) A
- ={ z is set to the pole α }=
- m α^(m-1) A
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