LogGamma[z] == Integrate[PolyGamma[t], {t, 1, z}]

Cell[BoxData[RowBox[List[RowBox[List["LogGamma", "[", "z", "]"]], "\[Equal]", RowBox[List[SubsuperscriptBox["\[Integral]", "1", "z"], RowBox[List[RowBox[List["PolyGamma", "[", "t", "]"]], RowBox[List["\[DifferentialD]", "t"]]]]]]]]]]

<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> log&#915; </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> </mstyle> <mo> &#10869; </mo> <mrow> <msubsup> <mo> &#8747; </mo> <mn> 1 </mn> <mi> z </mi> </msubsup> <mrow> <mrow> <semantics> <mi> &#968; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[Psi]&quot;, PolyGamma] </annotation> </semantics> <mo> ( </mo> <mi> t </mi> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> &#8518; </mo> <mi> t </mi> </mrow> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <times /> <ci> log&#915; </ci> <ci> z </ci> </apply> <apply> <int /> <bvar> <ci> t </ci> </bvar> <lowlimit> <cn type='integer'> 1 </cn> </lowlimit> <uplimit> <ci> z </ci> </uplimit> <apply> <ci> PolyGamma </ci> <ci> t </ci> </apply> </apply> </apply> </annotation-xml> </semantics> </math>

Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["LogGamma", "[", "z_", "]"]], "]"]], "\[RuleDelayed]", RowBox[List[SubsuperscriptBox["\[Integral]", "1", "z"], RowBox[List[RowBox[List["PolyGamma", "[", "t", "]"]], RowBox[List["\[DifferentialD]", "t"]]]]]]]]]]

2001-10-29