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variants of this functions
Gamma




Mathematica Notation

Traditional Notation









Gamma, Beta, Erf > Gamma[z] > Transformations > Products, sums, and powers of the direct function > Products of the direct function





http://functions.wolfram.com/06.05.16.0019.01









  


  








Input Form





Gamma[z] Gamma[n - z] == (Pi/Sin[Pi z]) Pochhammer[1 - z, n - 1] /; Element[n, Integers]








Standard Form





Cell[BoxData[RowBox[List[RowBox[List[RowBox[List[RowBox[List["Gamma", "[", "z", "]"]], " ", RowBox[List["Gamma", "[", RowBox[List["n", "-", "z"]], "]"]]]], "\[Equal]", RowBox[List[FractionBox["\[Pi]", RowBox[List[" ", RowBox[List["Sin", "[", RowBox[List["\[Pi]", " ", "z"]], "]"]]]]], RowBox[List["Pochhammer", "[", RowBox[List[RowBox[List["1", "-", "z"]], ",", RowBox[List["n", "-", "1"]]]], "]"]]]]]], "/;", RowBox[List["n", "\[Element]", "Integers"]]]]]]








MathML Form







<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <mrow> <mrow> <mi> &#915; </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mi> &#915; </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> n </mi> <mo> - </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> &#10869; </mo> <mrow> <mfrac> <mi> &#960; </mi> <mrow> <mi> sin </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> &#960; </mi> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mfrac> <mo> &#8290; </mo> <semantics> <msub> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mrow> <mi> n </mi> <mo> - </mo> <mn> 1 </mn> </mrow> </msub> <annotation encoding='Mathematica'> TagBox[SubscriptBox[RowBox[List[&quot;(&quot;, RowBox[List[&quot;1&quot;, &quot;-&quot;, &quot;z&quot;]], &quot;)&quot;]], RowBox[List[&quot;n&quot;, &quot;-&quot;, &quot;1&quot;]]], Pochhammer] </annotation> </semantics> </mrow> </mrow> <mo> /; </mo> <mrow> <mi> n </mi> <mo> &#8712; </mo> <semantics> <mi> &#8484; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[DoubleStruckCapitalZ]&quot;, Function[Integers]] </annotation> </semantics> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <times /> <apply> <ci> Gamma </ci> <ci> z </ci> </apply> <apply> <ci> Gamma </ci> <apply> <plus /> <ci> n </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> </apply> </apply> </apply> <apply> <times /> <apply> <times /> <pi /> <apply> <power /> <apply> <sin /> <apply> <times /> <pi /> <ci> z </ci> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <ci> Pochhammer </ci> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> </apply> <apply> <plus /> <ci> n </ci> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <apply> <in /> <ci> n </ci> <integers /> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[RowBox[List["Gamma", "[", "z_", "]"]], " ", RowBox[List["Gamma", "[", RowBox[List["n_", "-", "z_"]], "]"]]]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox[RowBox[List["\[Pi]", " ", RowBox[List["Pochhammer", "[", RowBox[List[RowBox[List["1", "-", "z"]], ",", RowBox[List["n", "-", "1"]]]], "]"]]]], RowBox[List["Sin", "[", RowBox[List["\[Pi]", " ", "z"]], "]"]]], "/;", RowBox[List["n", "\[Element]", "Integers"]]]]]]]]


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





2007-05-02