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Rising factorial
Notation$$n^{(x)}$$
TypeCombinatorial
Based onFactorial
Growth rate$$f_{2}(n)$$

The rising factorial $$x^{(n)}$$ is defined as $$x \cdot (x + 1) \cdot (x + 2) \cdot \ldots \cdot ((x + n) - 1)$$ .[1]

This function has a growth rate of about $$f_2(x)$$ in the FGH.

## Examples

$$x^{(1)}$$ = $$x$$

$$x^{(2)}$$ = $$x(x+1)$$=$$x^{2}+x$$

$$0^{(n)}$$ = $$0 \cdot 1 \cdot ...$$ = $$0$$