Pochhammer symbol: Representations through equivalent functions (formula 06.10.27.0001)

Pochhammer

$Mathematica Notation$

Gamma, Beta, Erf

Pochhammer[a,n]

Representations through equivalent functions

With related functions

http://functions.wolfram.com/06.10.27.0001.01

Input Form

Pochhammer[a, n] == Gamma[a + n]/Gamma[a]

Standard Form

Cell[BoxData[RowBox[List[RowBox[List["Pochhammer", "[", RowBox[List["a", ",", "n"]], "]"]], "\[Equal]", FractionBox[RowBox[List["Gamma", "[", RowBox[List["a", "+", "n"]], "]"]], RowBox[List["Gamma", "[", "a", "]"]]]]]]]

MathML Form

<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <semantics> <msub> <mrow> <mo> ( </mo> <mi> a </mi> <mo> ) </mo> </mrow> <mi> n </mi> </msub> <annotation encoding='Mathematica'> TagBox[SubscriptBox[RowBox[List["(", "a", ")"]], "n"], Pochhammer] </annotation> </semantics> <mo> ⩵ </mo> <mfrac> <mrow> <mi> Γ </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mi> a </mi> <mo> + </mo> <mi> n </mi> </mrow> <mo> ) </mo> </mrow> <mrow> <mi> Γ </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> a </mi> <mo> ) </mo> </mrow> </mfrac> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> Pochhammer </ci> <ci> a </ci> <ci> n </ci> </apply> <apply> <times /> <apply> <ci> Gamma </ci> <apply> <plus /> <ci> a </ci> <ci> n </ci> </apply> </apply> <apply> <power /> <apply> <ci> Gamma </ci> <ci> a </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </annotation-xml> </semantics> </math>

Rule Form

Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Pochhammer", "[", RowBox[List["a_", ",", "n_"]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List["Gamma", "[", RowBox[List["a", "+", "n"]], "]"]], RowBox[List["Gamma", "[", "a", "]"]]]]]]]

Date Added to functions.wolfram.com (modification date)

2001-10-29