HarmonicNumber[Conjugate[z]] == Conjugate[HarmonicNumber[z]]

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

<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <msub> <semantics> <mi> H </mi> <annotation-xml encoding='MathML-Content'> <ci> HarmonicNumber </ci> </annotation-xml> </semantics> <mover> <mi> z </mi> <mo> _ </mo> </mover> </msub> <mo> &#10869; </mo> <mover> <semantics> <msub> <mi> H </mi> <mi> z </mi> </msub> <annotation encoding='Mathematica'> TagBox[SubscriptBox[InterpretationBox[&quot;H&quot;, HarmonicNumber, Rule[Editable, False], Rule[Selectable, False]], &quot;z&quot;], PolyGamma] </annotation> </semantics> <mo> _ </mo> </mover> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> HarmonicNumber </ci> <apply> <ci> OverBar </ci> <ci> z </ci> </apply> </apply> <apply> <ci> OverBar </ci> <apply> <ci> PolyGamma </ci> <apply> <ci> HarmonicNumber </ci> <ci> z </ci> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>

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

2001-10-29