A q-analog, also called a q-extension or q-generalization, is a mathematical expression parameterized by a quantity q that generalizes a known expression and reduces to the known expression in the limit q->1^-. There are q-analogs of the factorial, binomial coefficient, derivative, integral, Fibonacci numbers, and so on. Koornwinder, Suslov, and Bustoz, have even managed some kind of q-Fourier analysis. Note that while European writers generally prefer the British spelling "q-analogue", American authors prefer the shorter "q-analog" (Andrews et al. 1999, pp. 490 and 496). To avoid this ambiguity (as well as the pitfall that there are sometimes more than just a single q-analog), the term q-extension (Andrews et al. 1999, pp. 483, 485, 487, etc.) may be preferable.
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