Logarithm of the gamma function: Transformations (formula 06.11.16.0003)

LogGamma

$Mathematica Notation$

Gamma, Beta, Erf

LogGamma[z]

Transformations

Transformations and argument simplifications

Argument involving basic arithmetic operations

http://functions.wolfram.com/06.11.16.0003.01

Input Form

LogGamma[z + 1] == LogGamma[z] + Log[z]

Standard Form

Cell[BoxData[RowBox[List[RowBox[List["LogGamma", "[", RowBox[List["z", "+", "1"]], "]"]], "\[Equal]", RowBox[List[RowBox[List["LogGamma", "[", "z", "]"]], "+", RowBox[List["Log", "[", "z", "]"]]]]]]]]

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> logΓ </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mi> z </mi> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> </mstyle> <mo> ⩵ </mo> <mrow> <mstyle scriptlevel='0'> <mrow> <mi> logΓ </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mstyle> <mo> + </mo> <mrow> <mi> log </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> LogGamma </ci> <apply> <plus /> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> </apply> <apply> <plus /> <apply> <times /> <ci> logΓ </ci> <ci> z </ci> </apply> <apply> <ln /> <ci> z </ci> </apply> </apply> </apply> </annotation-xml> </semantics> </math>

Rule Form

Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["LogGamma", "[", RowBox[List["z_", "+", "1"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["LogGamma", "[", "z", "]"]], "+", RowBox[List["Log", "[", "z", "]"]]]]]]]]

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

2001-10-29