Efficient Recursive Methods for Partial Fraction Expansion of General Rational Functions

Algorithm 2

Algorithm for functions in expanded form.

Step  1. calculate residues of using (59a) (59b).

 Step  1.1. calculate   directly

 For

  .

 End

 Step  1.2. calculate     using

 For

  For

  End

  For

   For

   End

  End

 End

Step 2. calculate the residues of using (64a) and (64b)

.

For

   For

    For

    End

   End

End

Step 3. calculate the residual polynomial coefficients of , using (79a) (79b).

 Step  3.1. = 1

 Step  3.2. calculate   using (79b)

 For

 End

 Step  3.3. Calculate     using (79a)

 For

End

Step 4. calculate the residual polynomial coefficients of using .