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LerchPhi




Mathematica Notation

Traditional Notation









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





http://functions.wolfram.com/10.06.03.0028.01









  


  








Input Form





LerchPhiClassicalRegularized[0, s, a] == (a^2)^(-s/2)








Standard Form





Cell[BoxData[RowBox[List[RowBox[List["LerchPhiClassicalRegularized", "[", RowBox[List["0", ",", "s", ",", "a"]], "]"]], "\[Equal]", SuperscriptBox[RowBox[List["(", SuperscriptBox["a", "2"], ")"]], RowBox[List[RowBox[List["-", "s"]], "/", "2"]]]]]]]








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> <mover> <mi> &#934; </mi> <mo> ~ </mo> </mover> <mo> ( </mo> <mrow> <mn> 0 </mn> <mo> , </mo> <mi> s </mi> <mo> , </mo> <mi> a </mi> </mrow> <mo> ) </mo> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List[OverscriptBox[&quot;\[CapitalPhi]&quot;, &quot;~&quot;], &quot;(&quot;, RowBox[List[TagBox[&quot;0&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, $CellContext`e3], LerchPhi[$CellContext`e1, $CellContext`e2, $CellContext`e3]]]] </annotation> </semantics> <mo> &#10869; </mo> <msup> <mrow> <mo> ( </mo> <msup> <mi> a </mi> <mn> 2 </mn> </msup> <mo> ) </mo> </mrow> <mrow> <mrow> <mo> - </mo> <mi> s </mi> </mrow> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> LerchPhi </ci> <cn type='integer'> 0 </cn> <ci> s </ci> <ci> a </ci> </apply> <apply> <power /> <apply> <power /> <ci> a </ci> <cn type='integer'> 2 </cn> </apply> <apply> <times /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> s </ci> </apply> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["LerchPhiClassicalRegularized", "[", RowBox[List["0", ",", "s_", ",", "a_"]], "]"]], "]"]], "\[RuleDelayed]", SuperscriptBox[RowBox[List["(", SuperscriptBox["a", "2"], ")"]], RowBox[List["-", FractionBox["s", "2"]]]]]]]]


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





2001-10-29