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http://functions.wolfram.com/10.06.16.0011.01
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LerchPhiClassical[z, s, m a] == Sum[LerchPhiClassical[z^m, s, a + k/m] z^k,
{k, 0, m - 1}]/m^s /; Element[m, Integers] && m > 1
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Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["LerchPhiClassical", "[", RowBox[List["z", ",", "s", ",", RowBox[List["m", " ", "a"]]]], "]"]], "\[Equal]", RowBox[List[SuperscriptBox["m", RowBox[List["-", "s"]]], RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "0"]], RowBox[List["m", "-", "1"]]], RowBox[List[RowBox[List["LerchPhiClassical", "[", RowBox[List[SuperscriptBox["z", "m"], ",", "s", ",", RowBox[List["a", "+", FractionBox["k", "m"]]]]], "]"]], SuperscriptBox["z", "k"]]]]]]]]], "/;", RowBox[List[RowBox[List["m", "\[Element]", "Integers"]], "\[And]", RowBox[List["m", ">", "1"]]]]]]]]
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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> <mrow> <semantics> <mrow> <mover> <mi> Φ </mi> <mo> ^ </mo> </mover> <mo> ( </mo> <mrow> <mi> z </mi> <mo> , </mo> <mi> s </mi> <mo> , </mo> <mrow> <mi> m </mi> <mo> ⁢ </mo> <mi> a </mi> </mrow> </mrow> <mo> ) </mo> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List[OverscriptBox["\[CapitalPhi]", "^"], "(", RowBox[List[TagBox["z", Rule[Editable, True]], ",", TagBox["s", Rule[Editable, True]], ",", TagBox[RowBox[List["m", " ", "a"]], Rule[Editable, True]]]], ")"]], InterpretTemplate[Function[List[$CellContext`a, $CellContext`b, $CellContext`c], LerchPhi[$CellContext`a, $CellContext`b, $CellContext`c]]]] </annotation> </semantics> <mo>  </mo> <mrow> <msup> <mi> m </mi> <mrow> <mo> - </mo> <mi> s </mi> </mrow> </msup> <mo> ⁢ </mo> <mrow> <munderover> <mo> ∑ </mo> <mrow> <mi> k </mi> <mo> = </mo> <mn> 0 </mn> </mrow> <mrow> <mi> m </mi> <mo> - </mo> <mn> 1 </mn> </mrow> </munderover> <mrow> <mrow> <mover> <mi> Φ </mi> <mo> ^ </mo> </mover> <mo> ( </mo> <mrow> <msup> <mi> z </mi> <mi> m </mi> </msup> <mo> , </mo> <mi> s </mi> <mo> , </mo> <mrow> <mi> a </mi> <mo> + </mo> <mfrac> <mi> k </mi> <mi> m </mi> </mfrac> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msup> <mi> z </mi> <mi> k </mi> </msup> </mrow> </mrow> </mrow> </mrow> <mo> /; </mo> <mrow> <mrow> <mi> m </mi> <mo> ∈ </mo> <semantics> <mi> ℤ </mi> <annotation encoding='Mathematica'> TagBox["\[DoubleStruckCapitalZ]", Function[List[], Integers]] </annotation> </semantics> </mrow> <mo> ∧ </mo> <mrow> <mi> m </mi> <mo> > </mo> <mn> 1 </mn> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <ci> LerchPhi </ci> <ci> z </ci> <ci> s </ci> <apply> <times /> <ci> m </ci> <ci> a </ci> </apply> </apply> <apply> <times /> <apply> <power /> <ci> m </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> s </ci> </apply> </apply> <apply> <sum /> <bvar> <ci> k </ci> </bvar> <lowlimit> <cn type='integer'> 0 </cn> </lowlimit> <uplimit> <apply> <plus /> <ci> m </ci> <cn type='integer'> -1 </cn> </apply> </uplimit> <apply> <times /> <apply> <apply> <ci> OverHat </ci> <ci> Φ </ci> </apply> <apply> <power /> <ci> z </ci> <ci> m </ci> </apply> <ci> s </ci> <apply> <plus /> <ci> a </ci> <apply> <times /> <ci> k </ci> <apply> <power /> <ci> m </ci> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <apply> <power /> <ci> z </ci> <ci> k </ci> </apply> </apply> </apply> </apply> </apply> <apply> <and /> <apply> <in /> <ci> m </ci> <integers /> </apply> <apply> <gt /> <ci> m </ci> <cn type='integer'> 1 </cn> </apply> </apply> </apply> </annotation-xml> </semantics> </math>
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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["LerchPhiClassical", "[", RowBox[List["z_", ",", "s_", ",", RowBox[List["m_", " ", "a_"]]]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[SuperscriptBox["m", RowBox[List["-", "s"]]], " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "0"]], RowBox[List["m", "-", "1"]]], RowBox[List[RowBox[List["LerchPhiClassical", "[", RowBox[List[SuperscriptBox["z", "m"], ",", "s", ",", RowBox[List["a", "+", FractionBox["k", "m"]]]]], "]"]], " ", SuperscriptBox["z", "k"]]]]]]], "/;", RowBox[List[RowBox[List["m", "\[Element]", "Integers"]], "&&", RowBox[List["m", ">", "1"]]]]]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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