|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
http://functions.wolfram.com/06.15.04.0002.02
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
PolyGamma[Conjugate[\[Nu]], Conjugate[z]] ==
Conjugate[PolyGamma[\[Nu], z]] /;
!IntervalMemberQ[Interval[{-Infinity, 0}], z]
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["PolyGamma", "[", RowBox[List[RowBox[List["Conjugate", "[", "\[Nu]", "]"]], ",", RowBox[List["Conjugate", "[", "z", "]"]]]], "]"]], "\[Equal]", RowBox[List["Conjugate", "[", RowBox[List["PolyGamma", "[", RowBox[List["\[Nu]", ",", "z"]], "]"]], "]"]]]], "/;", RowBox[List["Not", "[", RowBox[List["IntervalMemberQ", "[", RowBox[List[RowBox[List["Interval", "[", RowBox[List["{", RowBox[List[RowBox[List["-", "\[Infinity]"]], ",", "0"]], "}"]], "]"]], ",", "z"]], "]"]], "]"]]]]]]
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <mrow> <mstyle scriptlevel='0'> <msup> <semantics> <mi> ψ </mi> <annotation encoding='Mathematica'> TagBox["\[Psi]", PolyGamma] </annotation> </semantics> <mrow> <mo> ( </mo> <mstyle scriptlevel='0'> <mover> <mi> ν </mi> <mo> _ </mo> </mover> </mstyle> <mo> ) </mo> </mrow> </msup> </mstyle> <mo> ( </mo> <mstyle scriptlevel='0'> <mover> <mi> z </mi> <mo> _ </mo> </mover> </mstyle> <mstyle scriptlevel='0'> <mo> ) </mo> </mstyle> </mrow> <mstyle scriptlevel='0'> <mo> ⩵ </mo> </mstyle> <mover> <mstyle scriptlevel='0'> <semantics> <mrow> <mstyle scriptlevel='0'> <msup> <mi> ψ </mi> <mrow> <mo> ( </mo> <mi> ν </mi> <mo> ) </mo> </mrow> </msup> </mstyle> <mo> ( </mo> <mstyle scriptlevel='0'> <mi> z </mi> </mstyle> <mstyle scriptlevel='0'> <mo> ) </mo> </mstyle> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List[StyleBox[SuperscriptBox[TagBox["\[Psi]", PolyGamma], RowBox[List["(", "\[Nu]", ")"]]], Rule[ScriptLevel, 0]], "(", StyleBox["z", Rule[ScriptLevel, 0]], StyleBox[")", Rule[ScriptLevel, 0]]]], StirlingS1] </annotation> </semantics> </mstyle> <mo> _ </mo> </mover> </mrow> <mo> /; </mo> <mrow> <mi> z </mi> <mo> ∉ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mi> ∞ </mi> </mrow> <mo> , </mo> <mn> 0 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> FormBox </ci> <apply> <ci> RowBox </ci> <list> <apply> <ci> RowBox </ci> <list> <apply> <ci> RowBox </ci> <list> <apply> <ci> SuperscriptBox </ci> <apply> <ci> TagBox </ci> <ms> ψ </ms> <ci> PolyGamma </ci> </apply> <apply> <ci> RowBox </ci> <list> <ms> ( </ms> <apply> <ci> OverscriptBox </ci> <ms> ν </ms> <ms> _ </ms> </apply> <ms> ) </ms> </list> </apply> </apply> <ms> ( </ms> <apply> <ci> OverscriptBox </ci> <ms> z </ms> <ms> _ </ms> </apply> <ms> ) </ms> </list> </apply> <ms> ⩵ </ms> <apply> <ci> OverscriptBox </ci> <apply> <ci> ErrorBox </ci> <apply> <ci> TagBox </ci> <apply> <ci> RowBox </ci> <list> <apply> <ci> StyleBox </ci> <apply> <ci> SuperscriptBox </ci> <apply> <ci> TagBox </ci> <ms> ψ </ms> <ci> PolyGamma </ci> </apply> <apply> <ci> RowBox </ci> <list> <ms> ( </ms> <ms> ν </ms> <ms> ) </ms> </list> </apply> </apply> <apply> <ci> Rule </ci> <ci> ScriptLevel </ci> <cn type='integer'> 0 </cn> </apply> </apply> <ms> ( </ms> <apply> <ci> StyleBox </ci> <ms> z </ms> <apply> <ci> Rule </ci> <ci> ScriptLevel </ci> <cn type='integer'> 0 </cn> </apply> </apply> <apply> <ci> StyleBox </ci> <ms> ) </ms> <apply> <ci> Rule </ci> <ci> ScriptLevel </ci> <cn type='integer'> 0 </cn> </apply> </apply> </list> </apply> <ci> StirlingS1 </ci> </apply> </apply> <ms> _ </ms> </apply> </list> </apply> <ms> /; </ms> <apply> <ci> RowBox </ci> <list> <ms> z </ms> <ms> ∉ </ms> <apply> <ci> RowBox </ci> <list> <ms> ( </ms> <apply> <ci> RowBox </ci> <list> <apply> <ci> RowBox </ci> <list> <ms> - </ms> <ms> ∞ </ms> </list> </apply> <ms> , </ms> <ms> 0 </ms> </list> </apply> <ms> ) </ms> </list> </apply> </list> </apply> </list> </apply> <ci> TraditionalForm </ci> </apply> </annotation-xml> </semantics> </math>
|
|
|
|
|
|
|
|
|
|
| |
|
|
|
|
| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["PolyGamma", "[", RowBox[List[RowBox[List["Conjugate", "[", "\[Nu]_", "]"]], ",", RowBox[List["Conjugate", "[", "z_", "]"]]]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["Conjugate", "[", RowBox[List["PolyGamma", "[", RowBox[List["\[Nu]", ",", "z"]], "]"]], "]"]], "/;", RowBox[List["!", RowBox[List["IntervalMemberQ", "[", RowBox[List[RowBox[List["Interval", "[", RowBox[List["{", RowBox[List[RowBox[List["-", "\[Infinity]"]], ",", "0"]], "}"]], "]"]], ",", "z"]], "]"]]]]]]]]]] |
|
|
|
|
|
|
|
|
|
|
Date Added to functions.wolfram.com (modification date)
|
|
|
|
|
|
|
|
|
|
|
|
|
|