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variants of this functions
PolyLog




Mathematica Notation

Traditional Notation









Zeta Functions and Polylogarithms > PolyLog[nu,p,z] > General characteristics > Branch cuts > With respect to z





http://functions.wolfram.com/10.09.04.0008.01









  


  








Input Form





BranchCuts[PolyLog[\[Nu], p, z], z] == {{Interval[{1, Infinity}], I}} /; Element[\[Nu], Integers] && \[Nu] > 0 && Element[p, Integers] && p > 0








Standard Form





Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["BranchCuts", "[", RowBox[List[RowBox[List["PolyLog", "[", RowBox[List["\[Nu]", ",", "p", ",", "z"]], "]"]], ",", "z"]], "]"]], "\[Equal]", RowBox[List["{", RowBox[List["{", RowBox[List[RowBox[List["Interval", "[", RowBox[List["{", RowBox[List["1", ",", "\[Infinity]"]], "}"]], "]"]], ",", "\[ImaginaryI]"]], "}"]], "}"]]]], "/;", RowBox[List[RowBox[List["\[Nu]", "\[Element]", "Integers"]], "\[And]", RowBox[List["\[Nu]", ">", "0"]], "\[And]", RowBox[List["p", "\[Element]", "Integers"]], "\[And]", RowBox[List["p", ">", "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> &#8492;&#119966; </mi> <mi> z </mi> </msub> <mo> ( </mo> <mrow> <msub> <semantics> <mi> S </mi> <annotation-xml encoding='MathML-Content'> <ci> PolyLog </ci> </annotation-xml> </semantics> <mrow> <mi> &#957; </mi> <mo> , </mo> <mi> p </mi> </mrow> </msub> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> ) </mo> </mrow> <mo> &#10869; </mo> <mrow> <mo> { </mo> <mrow> <mo> { </mo> <mrow> <mrow> <mo> { </mo> <mrow> <mn> 1 </mn> <mo> , </mo> <mi> &#8734; </mi> </mrow> <mo> } </mo> </mrow> <mo> , </mo> <mi> &#8520; </mi> </mrow> <mo> } </mo> </mrow> <mo> } </mo> </mrow> </mrow> <mo> /; </mo> <mrow> <mrow> <mi> &#957; </mi> <mo> &#8712; </mo> <semantics> <msup> <mi> &#8469; </mi> <mo> + </mo> </msup> <annotation encoding='Mathematica'> TagBox[SuperscriptBox[&quot;\[DoubleStruckCapitalN]&quot;, &quot;+&quot;], Function[Integers]] </annotation> </semantics> </mrow> <mo> &#8743; </mo> <mrow> <mi> p </mi> <mo> &#8712; </mo> <semantics> <msup> <mi> &#8469; </mi> <mo> + </mo> </msup> <annotation encoding='Mathematica'> TagBox[SuperscriptBox[&quot;\[DoubleStruckCapitalN]&quot;, &quot;+&quot;], Function[Integers]] </annotation> </semantics> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <apply> <ci> Subscript </ci> <ci> &#8492;&#119966; </ci> <ci> z </ci> </apply> <apply> <ci> PolyLog </ci> <ci> &#957; </ci> <ci> p </ci> <ci> z </ci> </apply> </apply> <list> <list> <list> <cn type='integer'> 1 </cn> <infinity /> </list> <imaginaryi /> </list> </list> </apply> <apply> <and /> <apply> <in /> <ci> &#957; </ci> <integers /> </apply> <apply> <in /> <ci> p </ci> <integers /> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["BranchCuts", "[", RowBox[List[RowBox[List["PolyLog", "[", RowBox[List["\[Nu]_", ",", "p_", ",", "z_"]], "]"]], ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["{", RowBox[List["{", RowBox[List[RowBox[List["Interval", "[", RowBox[List["{", RowBox[List["1", ",", "\[Infinity]"]], "}"]], "]"]], ",", "\[ImaginaryI]"]], "}"]], "}"]], "/;", RowBox[List[RowBox[List["\[Nu]", "\[Element]", "Integers"]], "&&", RowBox[List["\[Nu]", ">", "0"]], "&&", RowBox[List["p", "\[Element]", "Integers"]], "&&", RowBox[List["p", ">", "0"]]]]]]]]]]


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





2001-10-29