Difference between revisions of "Falling factorial"

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(Created page with "The falling factorial $x^{\underline{k}}$ for nonnegative integer $k$ is given by $$x^{\underline{k}}=x(x-1)\ldots (x-k+1).$$")
 
 
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The falling factorial $x^{\underline{k}}$ for nonnegative [[integer]] $k$ is given by
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The falling factorial $x^{\underline{k}}$ for positive [[integer]] $k$ is given by
 
$$x^{\underline{k}}=x(x-1)\ldots (x-k+1).$$
 
$$x^{\underline{k}}=x(x-1)\ldots (x-k+1).$$
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If $k$ is not an integer, we use the following formula to interpret $x^{\underline{k}}$:
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$$x^{\underline{k}} = \dfrac{\Gamma(x+1)}{\Gamma(x-k+1)},$$
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where $\Gamma$ denotes the [[gamma function]].
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=Properties=
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=References=
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[[Category:SpecialFunction]]

Latest revision as of 12:27, 11 August 2016

The falling factorial $x^{\underline{k}}$ for positive integer $k$ is given by $$x^{\underline{k}}=x(x-1)\ldots (x-k+1).$$ If $k$ is not an integer, we use the following formula to interpret $x^{\underline{k}}$: $$x^{\underline{k}} = \dfrac{\Gamma(x+1)}{\Gamma(x-k+1)},$$ where $\Gamma$ denotes the gamma function.

Properties

References