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

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

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

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

Sources

See also

Main article: Factorial
Multifactorials: Double factorial · Multifactorial
Falling and rising: Falling factorial · Rising factorial
Other mathematical variants: Alternating factorial · Hyperfactorial · q-factorial · Roman factorial · Subfactorial · Weak factorial · Primorial · Compositorial · Semiprimorial
Tetrational growth: Exponential factorial · Expostfacto function · Superfactorial by Clifford Pickover
Nested Factorials: Tetorial · Petorial · Ectorial · Zettorial · Yottorial
Array-based extensions: Hyperfactorial array notation · Nested factorial notation
Other googological variants: · Superfactorial by Sloane and Plouffe · Torian · Factorexation · Mixed factorial · Bouncing Factorial
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