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http://functions.wolfram.com/10.06.03.0013.01
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LerchPhi[z, s, 5] == (-z - z^2/2^s - z^3/3^s - z^4/4^s + PolyLog[s, z])/z^5
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Cell[BoxData[RowBox[List[RowBox[List["LerchPhi", "[", RowBox[List["z", ",", "s", ",", "5"]], "]"]], "\[Equal]", FractionBox[RowBox[List[RowBox[List["-", "z"]], "-", RowBox[List[SuperscriptBox["2", RowBox[List["-", "s"]]], " ", SuperscriptBox["z", "2"]]], "-", RowBox[List[SuperscriptBox["3", RowBox[List["-", "s"]]], " ", SuperscriptBox["z", "3"]]], "-", RowBox[List[SuperscriptBox["4", RowBox[List["-", "s"]]], " ", SuperscriptBox["z", "4"]]], "+", RowBox[List["PolyLog", "[", RowBox[List["s", ",", "z"]], "]"]]]], SuperscriptBox["z", "5"]]]]]]
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<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <semantics> <mrow> <mi> Φ </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mi> z </mi> <mo> , </mo> <mi> s </mi> <mo> , </mo> <mn> 5 </mn> </mrow> <mo> ) </mo> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List["\[CapitalPhi]", "(", RowBox[List[TagBox["z", Rule[Editable, True]], ",", TagBox["s", Rule[Editable, True]], ",", "5"]], ")"]], InterpretTemplate[Function[List[$CellContext`e1, $CellContext`e2, $CellContext`e3], LerchPhi[$CellContext`e1, $CellContext`e2, $CellContext`e3]]]] </annotation> </semantics> <mo> ⩵ </mo> <mrow> <mfrac> <mn> 1 </mn> <msup> <mi> z </mi> <mn> 5 </mn> </msup> </mfrac> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <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> <mo> - </mo> <mi> z </mi> <mo> - </mo> <mrow> <msup> <mn> 2 </mn> <mrow> <mo> - </mo> <mi> s </mi> </mrow> </msup> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> - </mo> <mrow> <msup> <mn> 3 </mn> <mrow> <mo> - </mo> <mi> s </mi> </mrow> </msup> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 3 </mn> </msup> </mrow> <mo> - </mo> <mrow> <msup> <mn> 4 </mn> <mrow> <mo> - </mo> <mi> s </mi> </mrow> </msup> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 4 </mn> </msup> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <mrow> <semantics> <mrow> <mi> Φ </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mi> z </mi> <mo> , </mo> <mi> s </mi> <mo> , </mo> <mn> 5 </mn> </mrow> <mo> ) </mo> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List["\[CapitalPhi]", "(", RowBox[List[TagBox["z", Rule[Editable, True]], ",", TagBox["s", Rule[Editable, True]], ",", "5"]], ")"]], InterpretTemplate[Function[List[$CellContext`e1, $CellContext`e2, $CellContext`e3], LerchPhi[$CellContext`e1, $CellContext`e2, $CellContext`e3]]]] </annotation> </semantics> <mo> ⩵ </mo> <mrow> <mfrac> <mn> 1 </mn> <msup> <mi> z </mi> <mn> 5 </mn> </msup> </mfrac> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <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> <mo> - </mo> <mi> z </mi> <mo> - </mo> <mrow> <msup> <mn> 2 </mn> <mrow> <mo> - </mo> <mi> s </mi> </mrow> </msup> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> - </mo> <mrow> <msup> <mn> 3 </mn> <mrow> <mo> - </mo> <mi> s </mi> </mrow> </msup> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 3 </mn> </msup> </mrow> <mo> - </mo> <mrow> <msup> <mn> 4 </mn> <mrow> <mo> - </mo> <mi> s </mi> </mrow> </msup> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 4 </mn> </msup> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> </annotation-xml> </semantics> </math>
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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["LerchPhi", "[", RowBox[List["z_", ",", "s_", ",", "5"]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[RowBox[List["-", "z"]], "-", RowBox[List[SuperscriptBox["2", RowBox[List["-", "s"]]], " ", SuperscriptBox["z", "2"]]], "-", RowBox[List[SuperscriptBox["3", RowBox[List["-", "s"]]], " ", SuperscriptBox["z", "3"]]], "-", RowBox[List[SuperscriptBox["4", RowBox[List["-", "s"]]], " ", SuperscriptBox["z", "4"]]], "+", RowBox[List["PolyLog", "[", RowBox[List["s", ",", "z"]], "]"]]]], SuperscriptBox["z", "5"]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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