Given X(z) = z / (z - a)² with |z| a, the residue of X(z) z^-n-1 at z = a for n ≥ 0 will be

Question

Given X(z) = z / (z - a)² with |z| > a, the residue of X(z) z^-n-1 at z = a for n ≥ 0 will be

Accepted Answer

n a^(n-1). The residue of a function at a pole can be found using the formula for the residue at a pole of order greater than one. In this case, since the pole at z = a is of order 2, the residue is calculated as the coefficient of z^(-n-1) in the Laurent series expansion, which results in n a^(n-1).

Given X(z) = z / (z - a)² with |z| > a, the residue of X(z) z^-n-1 at z = a for n ≥ 0 will be

Solution

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