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http://functions.wolfram.com/06.11.16.0013.01
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LogGamma[3 z] == LogGamma[z] + LogGamma[z + 1/3] + LogGamma[z + 2/3] +
3 z Log[3] - Log[3]/2 - Log[2 Pi]
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Cell[BoxData[RowBox[List[RowBox[List["LogGamma", "[", RowBox[List["3", " ", "z"]], "]"]], "\[Equal]", RowBox[List[RowBox[List["LogGamma", "[", "z", "]"]], "+", RowBox[List["LogGamma", "[", RowBox[List["z", "+", FractionBox["1", "3"]]], "]"]], "+", RowBox[List["LogGamma", "[", RowBox[List["z", "+", FractionBox["2", "3"]]], "]"]], "+", RowBox[List["3", " ", "z", " ", RowBox[List["Log", "[", "3", "]"]]]], "-", FractionBox[RowBox[List["Log", "[", "3", "]"]], "2"], "-", RowBox[List["Log", "[", RowBox[List["2", " ", "\[Pi]"]], "]"]]]]]]]]
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<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <mi> logΓ </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 3 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mo>  </mo> <mrow> <mrow> <mi> logΓ </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> + </mo> <mrow> <mi> logΓ </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mi> z </mi> <mo> + </mo> <mfrac> <mn> 1 </mn> <mn> 3 </mn> </mfrac> </mrow> <mo> ) </mo> </mrow> <mo> + </mo> <mrow> <mi> logΓ </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mi> z </mi> <mo> + </mo> <mfrac> <mn> 2 </mn> <mn> 3 </mn> </mfrac> </mrow> <mo> ) </mo> </mrow> <mo> + </mo> <mrow> <mn> 3 </mn> <mo> ⁢ </mo> <mi> z </mi> <mo> ⁢ </mo> <mrow> <mi> log </mi> <mo> ⁡ </mo> <mo> ( </mo> <mn> 3 </mn> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mfrac> <mrow> <mi> log </mi> <mo> ⁡ </mo> <mo> ( </mo> <mn> 3 </mn> <mo> ) </mo> </mrow> <mn> 2 </mn> </mfrac> <mo> - </mo> <mrow> <mi> log </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> π </mi> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> LogGamma </ci> <apply> <times /> <cn type='integer'> 3 </cn> <ci> z </ci> </apply> </apply> <apply> <plus /> <apply> <ci> LogGamma </ci> <ci> z </ci> </apply> <apply> <ci> LogGamma </ci> <apply> <plus /> <ci> z </ci> <cn type='rational'> 1 <sep /> 3 </cn> </apply> </apply> <apply> <ci> LogGamma </ci> <apply> <plus /> <ci> z </ci> <cn type='rational'> 2 <sep /> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 3 </cn> <ci> z </ci> <apply> <ln /> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <ln /> <cn type='integer'> 3 </cn> </apply> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ln /> <apply> <times /> <cn type='integer'> 2 </cn> <pi /> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>
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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["LogGamma", "[", RowBox[List["3", " ", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["LogGamma", "[", "z", "]"]], "+", RowBox[List["LogGamma", "[", RowBox[List["z", "+", FractionBox["1", "3"]]], "]"]], "+", RowBox[List["LogGamma", "[", RowBox[List["z", "+", FractionBox["2", "3"]]], "]"]], "+", RowBox[List["3", " ", "z", " ", RowBox[List["Log", "[", "3", "]"]]]], "-", FractionBox[RowBox[List["Log", "[", "3", "]"]], "2"], "-", RowBox[List["Log", "[", RowBox[List["2", " ", "\[Pi]"]], "]"]]]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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){kind=small}
