Integrate[LogGamma[z], z] == PolyGamma[-2, z]

Cell[BoxData[RowBox[List[RowBox[List["\[Integral]", RowBox[List[RowBox[List["LogGamma", "[", "z", "]"]], RowBox[List["\[DifferentialD]", "z"]]]]]], "\[Equal]", RowBox[List["PolyGamma", "[", RowBox[List[RowBox[List["-", "2"]], ",", "z"]], "]"]]]]]]

<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <mo> &#8747; </mo> <mrow> <mrow> <mi> log&#915; </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> &#8518; </mo> <mi> z </mi> </mrow> </mrow> </mrow> <mo> &#63449; </mo> <mrow> <msup> <semantics> <mi> &#968; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[Psi]&quot;, PolyGamma] </annotation> </semantics> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <mn> 2 </mn> </mrow> <mo> ) </mo> </mrow> </msup> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <int /> <bvar> <ci> z </ci> </bvar> <apply> <ci> LogGamma </ci> <ci> z </ci> </apply> </apply> <apply> <ci> PolyGamma </ci> <cn type='integer'> -2 </cn> <ci> z </ci> </apply> </apply> </annotation-xml> </semantics> </math>

Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["\[Integral]", RowBox[List[RowBox[List["LogGamma", "[", "z_", "]"]], RowBox[List["\[DifferentialD]", "z_"]]]]]], "]"]], "\[RuleDelayed]", RowBox[List["PolyGamma", "[", RowBox[List[RowBox[List["-", "2"]], ",", "z"]], "]"]]]]]]

2007-05-02