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  1. Residue[π Cot[π z] f2[z], {z, k}] == f2[k]
  2.  
  3. Tr[Table[Residue[π Cot[π z] f2[z], {z, k}], {k, 0, 4}]]
  4.  
  5. f2[0] + f2[1] + f2[2] + f2[3] + f2[4]
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