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LerchPhi




Mathematica Notation

Traditional Notation









Zeta Functions and Polylogarithms > LerchPhi[z,s,a] > Specific values > Specialized values > For fixed z, s > For Phi(z,s,a)





http://functions.wolfram.com/10.06.03.0004.01









  


  








Input Form





LerchPhi[z, s, -3] == 3^(-s) + z/2^s + z^2 + z^3 PolyLog[s, z]








Standard Form





Cell[BoxData[RowBox[List[RowBox[List["LerchPhi", "[", RowBox[List["z", ",", "s", ",", RowBox[List["-", "3"]]]], "]"]], "\[Equal]", RowBox[List[SuperscriptBox["3", RowBox[List["-", "s"]]], "+", RowBox[List[SuperscriptBox["2", RowBox[List["-", "s"]]], " ", "z"]], "+", SuperscriptBox["z", "2"], "+", RowBox[List[SuperscriptBox["z", "3"], " ", RowBox[List["PolyLog", "[", RowBox[List["s", ",", "z"]], "]"]]]]]]]]]]








MathML Form







<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <semantics> <mrow> <mi> &#934; </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> z </mi> <mo> , </mo> <mi> s </mi> <mo> , </mo> <mrow> <mo> - </mo> <mn> 3 </mn> </mrow> </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[RowBox[List[&quot;-&quot;, &quot;3&quot;]], Rule[Editable, True]]]], &quot;)&quot;]], InterpretTemplate[Function[List[$CellContext`e1, $CellContext`e2, $CellContext`e3], LerchPhi[$CellContext`e1, $CellContext`e2, $CellContext`e3]]]] </annotation> </semantics> <mo> &#10869; </mo> <mrow> <mrow> <msup> <mi> z </mi> <mn> 3 </mn> </msup> <mo> &#8290; </mo> <mrow> <msub> <semantics> <mi> Li </mi> <annotation-xml encoding='MathML-Content'> <ci> PolyLog </ci> </annotation-xml> </semantics> <mi> s </mi> </msub> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> <mo> + </mo> <mrow> <msup> <mn> 2 </mn> <mrow> <mo> - </mo> <mi> s </mi> </mrow> </msup> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> + </mo> <msup> <mn> 3 </mn> <mrow> <mo> - </mo> <mi> s </mi> </mrow> </msup> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> LerchPhi </ci> <ci> z </ci> <ci> s </ci> <cn type='integer'> -3 </cn> </apply> <apply> <plus /> <apply> <times /> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> <apply> <ci> PolyLog </ci> <ci> s </ci> <ci> z </ci> </apply> </apply> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> <apply> <times /> <apply> <power /> <cn type='integer'> 2 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> s </ci> </apply> </apply> <ci> z </ci> </apply> <apply> <power /> <cn type='integer'> 3 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> s </ci> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["LerchPhi", "[", RowBox[List["z_", ",", "s_", ",", RowBox[List["-", "3"]]]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[SuperscriptBox["3", RowBox[List["-", "s"]]], "+", RowBox[List[SuperscriptBox["2", RowBox[List["-", "s"]]], " ", "z"]], "+", SuperscriptBox["z", "2"], "+", RowBox[List[SuperscriptBox["z", "3"], " ", RowBox[List["PolyLog", "[", RowBox[List["s", ",", "z"]], "]"]]]]]]]]]]


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





2001-10-29