Wolfram Researchfunctions.wolfram.comOther Wolfram Sites
Search Site
Function CategoriesGraphics GalleryNotationsGeneral IdentitiesAbout This Site ContributeEmail CommentsSign the Guestbook

View Related Information In
The Documentation Center

Download All Formulas For This Function
Mathematica Notebook
PDF File

Download All Introductions For This Function
Mathematica Notebook
PDF File


Developed with Mathematica -- Download a Free Trial Version

variants of this functions

Mathematica Notation

Traditional Notation

Gamma, Beta, Erf > PolyGamma[nu,z] > General characteristics > Symmetries and periodicities > Mirror symmetry




Input Form

PolyGamma[Conjugate[\[Nu]], Conjugate[z]] == Conjugate[PolyGamma[\[Nu], z]] /; !IntervalMemberQ[Interval[{-Infinity, 0}], z]

Standard Form

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"]], "]"]], "]"]]]]]]

MathML Form

<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> &#968; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[Psi]&quot;, PolyGamma] </annotation> </semantics> <mrow> <mo> ( </mo> <mstyle scriptlevel='0'> <mover> <mi> &#957; </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> &#10869; </mo> </mstyle> <mover> <mstyle scriptlevel='0'> <semantics> <mrow> <mstyle scriptlevel='0'> <msup> <mi> &#968; </mi> <mrow> <mo> ( </mo> <mi> &#957; </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[&quot;\[Psi]&quot;, PolyGamma], RowBox[List[&quot;(&quot;, &quot;\[Nu]&quot;, &quot;)&quot;]]], Rule[ScriptLevel, 0]], &quot;(&quot;, StyleBox[&quot;z&quot;, Rule[ScriptLevel, 0]], StyleBox[&quot;)&quot;, Rule[ScriptLevel, 0]]]], StirlingS1] </annotation> </semantics> </mstyle> <mo> _ </mo> </mover> </mrow> <mo> /; </mo> <mrow> <mi> z </mi> <mo> &#8713; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mi> &#8734; </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> &#968; </ms> <ci> PolyGamma </ci> </apply> <apply> <ci> RowBox </ci> <list> <ms> ( </ms> <apply> <ci> OverscriptBox </ci> <ms> &#957; </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> &#10869; </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> &#968; </ms> <ci> PolyGamma </ci> </apply> <apply> <ci> RowBox </ci> <list> <ms> ( </ms> <ms> &#957; </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> &#8713; </ms> <apply> <ci> RowBox </ci> <list> <ms> ( </ms> <apply> <ci> RowBox </ci> <list> <apply> <ci> RowBox </ci> <list> <ms> - </ms> <ms> &#8734; </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>

Rule Form

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)