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LerchPhi






Mathematica Notation

Traditional Notation









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





http://functions.wolfram.com/10.06.03.0017.02









  


  










Input Form





LerchPhi[z, -1, a] == (2 UnitStep[-Re[a]] - 1) ((a z - a - z)/(-1 + z)^2) + (UnitStep[-Re[a]] 2 (-((z (-1 + a (-1 + z) - (-1 + z) Ceiling[Re[a]]))/ (-1 + z)^2) + Sqrt[(a - Ceiling[Re[a]])^2] (1 - Ceiling[Re[a]] + Floor[Re[a]]) UnitStep[Im[a]]))/z^Ceiling[Re[a]]










Standard Form





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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> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <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[RowBox[List[&quot;-&quot;, &quot;1&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> <mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <msqrt> <msup> <mrow> <mo> ( </mo> <mrow> <mi> a </mi> <mo> - </mo> <mrow> <mo> &#8968; 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</mo> <mrow> <mo> ( </mo> <mrow> <mi> z </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mrow> <mrow> <mo> &#8968; </mo> <mrow> <mi> Re </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> a </mi> <mo> ) </mo> </mrow> <mo> &#8969; </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> z </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <msup> <mrow> <mo> ( </mo> <mrow> <mi> z </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> </mfrac> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <semantics> <mi> &#952; </mi> <annotation-xml encoding='MathML-Content'> <ci> UnitStep </ci> </annotation-xml> </semantics> <mo> ( </mo> <mrow> <mo> - </mo> <mrow> <mi> Re </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> a </mi> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msup> <mi> z </mi> <mrow> <mo> - </mo> <mrow> <mo> &#8968; </mo> <mrow> <mi> Re </mi> <mo> &#8289; 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Rule Form





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





2001-10-29





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