PolyGamma[Conjugate[z]] == Conjugate[PolyGamma[z]]

Cell[BoxData[RowBox[List[RowBox[List["PolyGamma", "[", RowBox[List["Conjugate", "[", "z", "]"]], "]"]], "\[Equal]", RowBox[List["Conjugate", "[", RowBox[List["PolyGamma", "[", "z", "]"]], "]"]]]]]]

<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <semantics> <mi> &#968; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[Psi]&quot;, PolyGamma] </annotation> </semantics> <mo> ( </mo> <mover> <mi> z </mi> <mo> _ </mo> </mover> <mo> ) </mo> </mrow> <mo> &#10869; </mo> <mover> <mrow> <semantics> <mi> &#968; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[Psi]&quot;, PolyGamma] </annotation> </semantics> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> _ </mo> </mover> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> PolyGamma </ci> <apply> <ci> OverBar </ci> <ci> z </ci> </apply> </apply> <apply> <ci> OverBar </ci> <apply> <ci> PolyGamma </ci> <ci> z </ci> </apply> </apply> </apply> </annotation-xml> </semantics> </math>

Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["PolyGamma", "[", RowBox[List["Conjugate", "[", "z_", "]"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List["Conjugate", "[", RowBox[List["PolyGamma", "[", "z", "]"]], "]"]]]]]]

2001-10-29