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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/06.05.16.0012.01









  


  








Input Form





Gamma[z] Gamma[-z] == -(Pi/(z Sin[Pi z]))








Standard Form





Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["Gamma", "[", "z", "]"]], " ", RowBox[List["Gamma", "[", RowBox[List["-", "z"]], "]"]]]], "\[Equal]", RowBox[List["-", FractionBox["\[Pi]", RowBox[List["z", " ", RowBox[List["Sin", "[", RowBox[List["\[Pi]", " ", "z"]], "]"]]]]]]]]]]]








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> <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> <mo> - </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> &#10869; </mo> <mrow> <mo> - </mo> <mfrac> <mi> &#960; </mi> <mrow> <mi> z </mi> <mo> &#8290; </mo> <mrow> <mi> sin </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> &#960; </mi> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> </mfrac> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <times /> <apply> <ci> Gamma </ci> <ci> z </ci> </apply> <apply> <ci> Gamma </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <pi /> <apply> <power /> <apply> <times /> <ci> z </ci> <apply> <sin /> <apply> <times /> <pi /> <ci> z </ci> </apply> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </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["-", "z_"]], "]"]]]], "]"]], "\[RuleDelayed]", RowBox[List["-", FractionBox["\[Pi]", RowBox[List["z", " ", RowBox[List["Sin", "[", RowBox[List["\[Pi]", " ", "z"]], "]"]]]]]]]]]]]


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





2001-10-29