d-Analog

The $d$-analog of Infinity Factorial is given by

$$[\infty!]_d=\prod_{n=3}^\infty \left({1-{2^d\over n^d}}\right).$$

This Infinite Product can be evaluated in closed form for small Positive integral $d\geq 2$.

See also q-Analog

References

Finch, S. ``Favorite Mathematical Constants.'' http://www.mathsoft.com/asolve/constant/infprd/infprd.html