Logarithm of the gamma function: Specific values (formula 06.11.03.0023)

LogGamma

$Mathematica Notation$

Gamma, Beta, Erf

LogGamma[z]

Specific values

Values at fixed points

http://functions.wolfram.com/06.11.03.0023.01

Input Form

LogGamma[1/2] == Log[Pi]/2

Standard Form

Cell[BoxData[RowBox[List[RowBox[List["LogGamma", "[", FractionBox["1", "2"], "]"]], "\[Equal]", 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> <mrow> <mi> logΓ </mi> <mo> ⁡ </mo> <mo> ( </mo> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> <mo> ) </mo> </mrow> <mo> ⩵ </mo> <mfrac> <mrow> <mi> log </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> π </mi> <mo> ) </mo> </mrow> <mn> 2 </mn> </mfrac> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> LogGamma </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <times /> <apply> <ln /> <pi /> </apply> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </annotation-xml> </semantics> </math>

Rule Form

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

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

2001-10-29