LogGamma[1/4] + LogGamma[3/4] == Log[2]/2 + Log[Pi]

Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["LogGamma", "[", FractionBox["1", "4"], "]"]], "+", RowBox[List["LogGamma", "[", FractionBox["3", "4"], "]"]]]], "\[Equal]", RowBox[List[FractionBox[RowBox[List["Log", "[", "2", "]"]], "2"], "+", RowBox[List["Log", "[", "\[Pi]", "]"]]]]]]]]

<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <mrow> <mi> log&#915; </mi> <mo> &#8289; </mo> <mo> ( </mo> <mfrac> <mn> 1 </mn> <mn> 4 </mn> </mfrac> <mo> ) </mo> </mrow> <mo> + </mo> <mrow> <mi> log&#915; </mi> <mo> &#8289; </mo> <mo> ( </mo> <mfrac> <mn> 3 </mn> <mn> 4 </mn> </mfrac> <mo> ) </mo> </mrow> </mrow> <mo> &#63449; </mo> <mrow> <mfrac> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mn> 2 </mn> <mo> ) </mo> </mrow> <mn> 2 </mn> </mfrac> <mo> + </mo> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> &#960; </mi> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <plus /> <apply> <ci> LogGamma </ci> <cn type='rational'> 1 <sep /> 4 </cn> </apply> <apply> <ci> LogGamma </ci> <cn type='rational'> 3 <sep /> 4 </cn> </apply> </apply> <apply> <plus /> <apply> <times /> <apply> <ln /> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <ln /> <pi /> </apply> </apply> </apply> </annotation-xml> </semantics> </math>

Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[RowBox[List["LogGamma", "[", FractionBox["1", "4"], "]"]], "+", RowBox[List["LogGamma", "[", FractionBox["3", "4"], "]"]]]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox[RowBox[List["Log", "[", "2", "]"]], "2"], "+", RowBox[List["Log", "[", "\[Pi]", "]"]]]]]]]]

2007-05-02