LogGamma[z] == D[PolyGamma[\[Nu], z], {z, -\[Nu] - 1}]

Cell[BoxData[RowBox[List[RowBox[List["LogGamma", "[", "z", "]"]], "\[Equal]", RowBox[List[SubscriptBox["\[PartialD]", RowBox[List["{", RowBox[List["z", ",", RowBox[List[RowBox[List["-", "\[Nu]"]], "-", "1"]]]], "}"]]], RowBox[List["PolyGamma", "[", RowBox[List["\[Nu]", ",", "z"]], "]"]]]]]]]]

<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> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mstyle> <mo> &#10869; </mo> <mfrac> <mrow> <msup> <mo> &#8706; </mo> <mrow> <mrow> <mo> - </mo> <mi> &#957; </mi> </mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mrow> <msup> <semantics> <mi> &#968; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[Psi]&quot;, PolyGamma] </annotation> </semantics> <mrow> <mo> ( </mo> <mi> &#957; </mi> <mo> ) </mo> </mrow> </msup> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> <mrow> <mo> &#8706; </mo> <msup> <mi> z </mi> <mrow> <mrow> <mo> - </mo> <mi> &#957; </mi> </mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> </mrow> </mfrac> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <times /> <ci> log&#915; </ci> <ci> z </ci> </apply> <apply> <partialdiff /> <bvar> <ci> z </ci> <degree> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> &#957; </ci> </apply> <cn type='integer'> -1 </cn> </apply> </degree> </bvar> <apply> <ci> PolyGamma </ci> <ci> &#957; </ci> <ci> z </ci> </apply> </apply> </apply> </annotation-xml> </semantics> </math>

Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["LogGamma", "[", "z_", "]"]], "]"]], "\[RuleDelayed]", RowBox[List[SubscriptBox["\[PartialD]", RowBox[List[RowBox[List["{", RowBox[List["z", ",", RowBox[List[RowBox[List["-", "\[Nu]"]], "-", "1"]]]], "}"]]]]], RowBox[List["PolyGamma", "[", RowBox[List["\[Nu]", ",", "z"]], "]"]]]]]]]]

2001-10-29