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) = iΠ(1) = i | i | Π(-i, 1) = - iΠ(1) = - i | -i |
2 | Π(i, 2) = - Π(2) = - 2 | -1 | Π(-i, 2) = - Π(2) = - 2 | -1 |
3 | Π(i, 3) = - iΠ(3) = - 6i | -i | Π(-i, 3) = iΠ(3) = 6i | i |
4 | Π(i, 4) = Π(4) = 24 | 1 | Π(-i, 4) = Π(4) = 24 | 1 |