lytic continuation from integer ``n``
to complex ``z`` (not only satisfying the functional equation but also
being logarithmically convex, c.f. Bohr-Mollerup theorem) -- in fact, the
choice of ``r`` above only changes the function by a constant factor. The
final constraint that determines the canonical continuation is ``f(1) = 1``,
which forces ``r = 1`` (see also [1]).::

  z!(k) = k ** ((z - 1)/k) * gamma(z/k + 1) / gamma(1/k + 1)

References
----------
.. [1] Complex extension to multifactorial
        https://en.wikipedia.org/wiki/Double_factorial#Alternative_extension_of_the_multifactorial
r>