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variants of this functions
PolyGamma




Mathematica Notation

Traditional Notation









Gamma, Beta, Erf > PolyGamma[nu,z] > General characteristics > Poles and essential singularities > With respect to z





http://functions.wolfram.com/06.15.04.0018.01









  


  








Input Form





Singularities[PolyGamma[\[Nu], z], z] == {} /; !(Element[\[Nu], Integers] && \[Nu] >= 0)








Standard Form





Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["Singularities", "[", RowBox[List[RowBox[List["PolyGamma", "[", RowBox[List["\[Nu]", ",", "z"]], "]"]], ",", "z"]], "]"]], "\[Equal]", RowBox[List["{", "}"]]]], "/;", RowBox[List["Not", "[", RowBox[List[RowBox[List["\[Nu]", "\[Element]", "Integers"]], "\[And]", RowBox[List["\[Nu]", "\[GreaterEqual]", "0"]]]], "]"]]]]]]








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> <msub> <mi> &#119982;&#119998;&#120003;&#8458; </mi> <mi> z </mi> </msub> <mo> ( </mo> <mrow> <mstyle scriptlevel='0'> <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> </mstyle> <mo> ( </mo> <mstyle scriptlevel='0'> <mi> z </mi> </mstyle> <mstyle scriptlevel='0'> <mo> ) </mo> </mstyle> </mrow> <mo> ) </mo> </mrow> <mo> &#10869; </mo> <mrow> <mo> { </mo> <mo> } </mo> </mrow> </mrow> <mo> /; </mo> <mrow> <mi> &#957; </mi> <mo> &#8713; </mo> <mi> &#8469; </mi> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <apply> <ci> Subscript </ci> <ci> &#119982;&#119998;&#120003;&#8458; </ci> <ci> z </ci> </apply> <apply> <ci> PolyGamma </ci> <ci> &#957; </ci> <ci> z </ci> </apply> </apply> <list /> </apply> <apply> <notin /> <ci> &#957; </ci> <ci> &#8469; </ci> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Singularities", "[", RowBox[List[RowBox[List["PolyGamma", "[", RowBox[List["\[Nu]_", ",", "z_"]], "]"]], ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["{", "}"]], "/;", RowBox[List["!", RowBox[List["(", RowBox[List[RowBox[List["\[Nu]", "\[Element]", "Integers"]], "&&", RowBox[List["\[Nu]", "\[GreaterEqual]", "0"]]]], ")"]]]]]]]]]]


Date Added to functions.wolfram.com (modification date)





2007-05-02