Rising factorial | |
---|---|
Notation | \(n^{(x)}\) |
Type | Combinatorial |
Based on | Factorial |
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 · MultifactorialFalling 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: · Tetrofactorial · Superfactorial by Sloane and Plouffe · Torian · Factorexation · Mixed factorial · Bouncing Factorial