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variants of this functions
Gamma




Mathematica Notation

Traditional Notation









Gamma, Beta, Erf > Gamma[z] > Representations through equivalent functions > With related functions





http://functions.wolfram.com/06.05.27.0002.01









  


  








Input Form





Gamma[z] == 2^((1/4) (3 - 4 z + Cos[2 Pi z])) Pi^((1/2) Sin[Pi z]^2) (2 z - 2)!!








Standard Form





Cell[BoxData[RowBox[List[RowBox[List["Gamma", "[", "z", "]"]], "\[Equal]", RowBox[List[SuperscriptBox["2", RowBox[List[FractionBox["1", "4"], " ", RowBox[List["(", RowBox[List["3", "-", RowBox[List["4", " ", "z"]], "+", RowBox[List["Cos", "[", RowBox[List["2", " ", "\[Pi]", " ", "z"]], "]"]]]], ")"]]]]], " ", SuperscriptBox["\[Pi]", RowBox[List[FractionBox["1", "2"], " ", SuperscriptBox[RowBox[List["Sin", "[", RowBox[List["\[Pi]", " ", "z"]], "]"]], "2"]]]], " ", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["2", " ", "z"]], "-", "2"]], ")"]], "!!"]]]]]]]]








MathML Form







<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <mi> &#915; </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> &#10869; </mo> <mrow> <msup> <mn> 2 </mn> <mrow> <mfrac> <mn> 1 </mn> <mn> 4 </mn> </mfrac> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mn> 3 </mn> <mo> - </mo> <mrow> <mn> 4 </mn> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> + </mo> <mrow> <mi> cos </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> &#960; </mi> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </msup> <mo> &#8290; </mo> <msup> <mi> &#960; </mi> <mrow> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> <mo> &#8290; </mo> <mrow> <msup> <mi> sin </mi> <mn> 2 </mn> </msup> <mo> ( </mo> <mrow> <mi> &#960; </mi> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> </msup> <mo> &#8290; </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> - </mo> <mn> 2 </mn> </mrow> <mo> ) </mo> </mrow> <mo> !! </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> Gamma </ci> <ci> z </ci> </apply> <apply> <times /> <apply> <power /> <cn type='integer'> 2 </cn> <apply> <times /> <cn type='rational'> 1 <sep /> 4 </cn> <apply> <plus /> <cn type='integer'> 3 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 4 </cn> <ci> z </ci> </apply> </apply> <apply> <cos /> <apply> <times /> <cn type='integer'> 2 </cn> <pi /> <ci> z </ci> </apply> </apply> </apply> </apply> </apply> <apply> <power /> <pi /> <apply> <times /> <cn type='rational'> 1 <sep /> 2 </cn> <apply> <power /> <apply> <sin /> <apply> <times /> <pi /> <ci> z </ci> </apply> </apply> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <ci> Factorial2 </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> z </ci> </apply> <cn type='integer'> -2 </cn> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Gamma", "[", "z_", "]"]], "]"]], "\[RuleDelayed]", RowBox[List[SuperscriptBox["2", RowBox[List[FractionBox["1", "4"], " ", RowBox[List["(", RowBox[List["3", "-", RowBox[List["4", " ", "z"]], "+", RowBox[List["Cos", "[", RowBox[List["2", " ", "\[Pi]", " ", "z"]], "]"]]]], ")"]]]]], " ", SuperscriptBox["\[Pi]", RowBox[List[FractionBox["1", "2"], " ", SuperscriptBox[RowBox[List["Sin", "[", RowBox[List["\[Pi]", " ", "z"]], "]"]], "2"]]]], " ", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["2", " ", "z"]], "-", "2"]], ")"]], "!!"]]]]]]]]


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





2001-10-29