The d-analog of a complex number s is defined as [s]_d = 1 - 2^d/s^d . For integer n, [2]! congruent 1 and [n]_d ! | = | [3][4]...[n] | = | (1 - 2^d/3^d)(1 - 2^d/4^d)...(1 - 2^d/n^d). It can then be extended to complex values via [s]_d ! = product_(j = 1)^∞ [j + 2]/[j + s] .

infinite product | q-analog