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Table 5 Periodicity of factorials of imaginary numbers

From: Factorials of real negative and imaginary numbers - A new perspective

Z (iz) ! Coeff. (-iz) ! Coeff.
1 Π(i, 1) = (1) = i i Π(-i, 1) = - (1) = - i -i
2 Π(i, 2) = - Π(2) = - 2 -1 Π(-i, 2) = - Π(2) = - 2 -1
3 Π(i, 3) = - (3) = - 6i -i Π(-i, 3) = (3) = 6i i
4 Π(i, 4) = Π(4) = 24 1 Π(-i, 4) = Π(4) = 24 1