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LogGamma




Mathematica Notation

Traditional Notation









Gamma, Beta, Erf > LogGamma[z] > Transformations > Multiple arguments > Argument involving numeric multiples of variable





http://functions.wolfram.com/06.11.16.0007.01









  


  








Input Form





LogGamma[2 z] == LogGamma[z] + LogGamma[z + 1/2] + Log[2] (2 z - 1) - Log[Pi]/2








Standard Form





Cell[BoxData[RowBox[List[RowBox[List["LogGamma", "[", RowBox[List["2", " ", "z"]], "]"]], "\[Equal]", RowBox[List[RowBox[List["LogGamma", "[", "z", "]"]], "+", RowBox[List["LogGamma", "[", RowBox[List["z", "+", FractionBox["1", "2"]]], "]"]], "+", RowBox[List[RowBox[List["Log", "[", "2", "]"]], RowBox[List["(", RowBox[List[RowBox[List["2", "z"]], "-", "1"]], ")"]]]], "-", FractionBox[RowBox[List["Log", "[", "\[Pi]", "]"]], "2"]]]]]]]








MathML Form







<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mstyle scriptlevel='0'> <mrow> <mi> log&#915; </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mstyle> <mo> &#10869; </mo> <mrow> <mrow> <mstyle scriptlevel='0'> <mi> log&#915; </mi> </mstyle> <mstyle scriptlevel='0'> <mo> ( </mo> </mstyle> <mrow> <mi> z </mi> <mo> + </mo> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> </mrow> <mo> ) </mo> </mrow> <mo> + </mo> <mstyle scriptlevel='0'> <mrow> <mi> log&#915; </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mstyle> <mo> + </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mn> 2 </mn> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mfrac> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> &#960; </mi> <mo> ) </mo> </mrow> <mn> 2 </mn> </mfrac> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> LogGamma </ci> <apply> <times /> <cn type='integer'> 2 </cn> <ci> z </ci> </apply> </apply> <apply> <plus /> <apply> <ci> LogGamma </ci> <apply> <plus /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <ci> log&#915; </ci> <ci> z </ci> </apply> <apply> <times /> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> z </ci> </apply> <cn type='integer'> -1 </cn> </apply> <apply> <ln /> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <ln /> <pi /> </apply> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["LogGamma", "[", RowBox[List["2", " ", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["LogGamma", "[", "z", "]"]], "+", RowBox[List["LogGamma", "[", RowBox[List["z", "+", FractionBox["1", "2"]]], "]"]], "+", RowBox[List[RowBox[List["Log", "[", "2", "]"]], " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "z"]], "-", "1"]], ")"]]]], "-", FractionBox[RowBox[List["Log", "[", "\[Pi]", "]"]], "2"]]]]]]]


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





2001-10-29