### Method

As can be seen from the code listing, this implementation of`residuez`simply calls

`residue`, which was written to carry out the partial fraction expansions of -plane (continuous-time) transfer functions :

where is the order of the quotient polynomial in , and is the

*multiplicity*of the th pole. (When all poles are distinct, we have for all .) For , we define . In the discrete-time case, we have the -plane transfer function

For compatibility with Matlab's

`residuez`, we need a PFE of the form such that

`B`and

`A`in the call to

`residue`. In the returned result, we obtain terms such as

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Example with Repeated Poles

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The Padé-Prony Method