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Table 6 Fractional factorials and multifactorials

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

Fractional factorials and multifactorials of real positive numbers
  Fractional factorials Multifactorials
z z! (0.5z)! (1.5z)! (2z)!! (3z)!!!
0 1 1 1 1 1
0.5 0.886 0.626 1.085 1.253 1.534
1 1 0.5 1.5 2 3
1.5 1.329 0.469 2.442 3.759 6.907
2 2 0.5 4.5 8 18
2.5 3.323 0.587 9.158 18.799 51.805
3 6 0.75 20.25 48 162
Fractional factorials and multifactorials of real negative numbers
  Fractional factorials Multifactorials
z (-z)! (-0.5)z! (-1.5z)! (-2z)!! (-3z)!!!
0 1 1 1 1 1
0.5 0.886i 0.626i 1.085 1.253i 1.534i
1 -1 -0.5 -1.5 -2 -3
1.5 -0.139i -0.469i -2.442 -3.759i -6.907i
2 2 0.5 4.5 8 18
2.5 3.323i 0.587 9.157 18.799i 51.805i
3 -6 -0.75 -20.25 -48 -162
Fractional factorials and multifactorials of imaginary positive numbers
  Fractional factorials Multifactorials
z (iz!) (0.5iz)! (1.5iz)! (2iz)!! (3iz)!!!
0 1 1 1 1 1
0.5 0.626 + 0.626i 0.443 + 0.443i 0.767 + 0.767i 0.886 + 0.886i 1.085 + 1.085i
1 i 0.5i 1.5i 2i 3i
1.5 -0.939 + 0.939i -0.332 + 0.332i -1.726 + 1.726i -2.658 + 2.658i -4.862 + 4.862i
2 -2 -0.5 -4.5 -8 -18
2.5 -2.349-2.349i -0.415-0.415i -6.475-6.475i -13.29-13.29i 36.6-36.6i
3 6i -0.75i -20.25i -48i -162i
Fractional factorials and multifactorials of imaginary negative numbers
  Fractional factorials Multifactorials
z (-iz)! (-0.5iz)! (-1.5iz)! (-2iz)!! (-3iz)!!!
0 1 1 1 1 1
0.5 0.626-0.626i 0.443-0.443i 0.767-0.767i 0.886-0.886i 1.085-1.085i
1 -i -0.5i -1.5i -2i -3i
1.5 -0.939-0.939i -0.332-0.332i -1.726-1.726i -2.658-2.658i -4.862-4.862i
2 -2 -0.5 -4.5 -8 -18
2.5 -2.349 + 2.349i -0.415 + 0.415i -6.475 + 6.475i -13.29 + 13.29i -36.6 + 36.6i
3 6i 0.75i 20.25i 48i 162i