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LerchPhi




Mathematica Notation

Traditional Notation









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





http://functions.wolfram.com/10.06.03.0033.01









  


  








Input Form





LerchPhi[1, s, 1] == Zeta[s] /; Re[s] > 1








Standard Form





Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["LerchPhi", "[", RowBox[List["1", ",", "s", ",", "1"]], "]"]], "\[Equal]", RowBox[List["Zeta", "[", "s", "]"]]]], "/;", RowBox[List[RowBox[List["Re", "[", "s", "]"]], ">", "1"]]]]]]








MathML Form







<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <semantics> <mrow> <mi> &#934; </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> , </mo> <mi> s </mi> <mo> , </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List[&quot;\[CapitalPhi]&quot;, &quot;(&quot;, RowBox[List[TagBox[&quot;1&quot;, Rule[Editable, True]], &quot;,&quot;, TagBox[&quot;s&quot;, Rule[Editable, True]], &quot;,&quot;, TagBox[&quot;1&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> <semantics> <mrow> <mi> &#950; </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> s </mi> <mo> ) </mo> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List[&quot;\[Zeta]&quot;, &quot;(&quot;, TagBox[&quot;s&quot;, Rule[Editable, True]], &quot;)&quot;]], InterpretTemplate[Function[$CellContext`e, Zeta[$CellContext`e]]]] </annotation> </semantics> </mrow> <mo> /; </mo> <mrow> <mrow> <mi> Re </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> s </mi> <mo> ) </mo> </mrow> <mo> &gt; </mo> <mn> 1 </mn> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <ci> LerchPhi </ci> <cn type='integer'> 1 </cn> <ci> s </ci> <cn type='integer'> 1 </cn> </apply> <apply> <ci> Zeta </ci> <ci> s </ci> </apply> </apply> <apply> <gt /> <apply> <real /> <ci> s </ci> </apply> <cn type='integer'> 1 </cn> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["LerchPhi", "[", RowBox[List["1", ",", "s_", ",", "1"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["Zeta", "[", "s", "]"]], "/;", RowBox[List[RowBox[List["Re", "[", "s", "]"]], ">", "1"]]]]]]]]


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





2001-10-29