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LerchPhi




Mathematica Notation

Traditional Notation









Zeta Functions and Polylogarithms > LerchPhi[z,s,a] > General characteristics > Poles and essential singularities > With respect to s > For Phi(z,s,a)





http://functions.wolfram.com/10.06.04.0007.01









  


  








Input Form





Singularities[LerchPhi[(Editable -> True)[z], (Editable -> True)[s], (Editable -> True)[a]], s] == {{ComplexInfinity, Infinity}}








Standard Form





Cell[BoxData[RowBox[List[RowBox[List["Singularities", "[", RowBox[List[RowBox[List["LerchPhi", "[", RowBox[List[TagBox["z", Rule[Editable, True]], ",", TagBox["s", Rule[Editable, True]], ",", TagBox["a", Rule[Editable, True]]]], "]"]], ",", "s"]], "]"]], "\[Equal]", RowBox[List["{", RowBox[List["{", RowBox[List["ComplexInfinity", ",", "\[Infinity]"]], "}"]], "}"]]]]]]








MathML Form







<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <msub> <mi> &#119982;&#119998;&#120003;&#8458; </mi> <mi> s </mi> </msub> <mo> ( </mo> <semantics> <mrow> <mi> &#934; </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> z </mi> <mo> , </mo> <mi> s </mi> <mo> , </mo> <mi> a </mi> </mrow> <mo> ) </mo> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List[&quot;\[CapitalPhi]&quot;, &quot;(&quot;, RowBox[List[TagBox[&quot;z&quot;, Rule[Editable, True]], &quot;,&quot;, TagBox[&quot;s&quot;, Rule[Editable, True]], &quot;,&quot;, TagBox[&quot;a&quot;, Rule[Editable, True]]]], &quot;)&quot;]], InterpretTemplate[Function[List[$CellContext`e1, $CellContext`e2], Zeta[$CellContext`e1, $CellContext`e2]]]] </annotation> </semantics> <mo> ) </mo> </mrow> <mo> &#10869; </mo> <mrow> <mo> { </mo> <mrow> <mo> { </mo> <mrow> <mover> <mi> &#8734; </mi> <mo> ~ </mo> </mover> <mo> , </mo> <mi> &#8734; </mi> </mrow> <mo> } </mo> </mrow> <mo> } </mo> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <apply> <ci> Subscript </ci> <ci> &#119982;&#119998;&#120003;&#8458; </ci> <ci> s </ci> </apply> <apply> <ci> Zeta </ci> <ci> z </ci> <ci> s </ci> </apply> </apply> <list> <list> <apply> <ci> OverTilde </ci> <infinity /> </apply> <infinity /> </list> </list> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Singularities", "[", RowBox[List[RowBox[List["LerchPhi", "[", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List["Editable", "\[Rule]", "True"]], ")"]], "[", "z_", "]"]], ",", RowBox[List[RowBox[List["(", RowBox[List["Editable", "\[Rule]", "True"]], ")"]], "[", "s_", "]"]], ",", RowBox[List[RowBox[List["(", RowBox[List["Editable", "\[Rule]", "True"]], ")"]], "[", "a_", "]"]]]], "]"]], ",", "s_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List["{", RowBox[List["{", RowBox[List["ComplexInfinity", ",", "\[Infinity]"]], "}"]], "}"]]]]]]


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





2001-10-29