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http://functions.wolfram.com/10.06.25.0002.01
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Limit[LerchPhiClassical[z, 1, a]/Log[1 - z], z -> 1] == -1
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Cell[BoxData[RowBox[List[RowBox[List["Limit", "[", RowBox[List[FractionBox[RowBox[List[" ", RowBox[List["LerchPhiClassical", "[", RowBox[List["z", ",", "1", ",", "a"]], "]"]]]], RowBox[List["Log", "[", RowBox[List["1", "-", "z"]], "]"]]], ",", RowBox[List["z", "\[Rule]", "1"]]]], "]"]], "\[Equal]", RowBox[List["-", "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> <munder> <mi> lim </mi> <mrow> <mi> z </mi> <semantics> <mo> → </mo> <annotation encoding='Mathematica'> "\[Rule]" </annotation> </semantics> <mn> 1 </mn> </mrow> </munder> <mo> ⁢ </mo> <mtext>   </mtext> <mfrac> <semantics> <mrow> <mover> <mi> Φ </mi> <mo> ^ </mo> </mover> <mo> ( </mo> <mrow> <mi> z </mi> <mo> , </mo> <mn> 1 </mn> <mo> , </mo> <mi> a </mi> </mrow> <mo> ) </mo> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List[OverscriptBox["\[CapitalPhi]", "^"], "(", RowBox[List[TagBox["z", Rule[Editable, True]], ",", TagBox["1", Rule[Editable, True]], ",", TagBox["a", Rule[Editable, True]]]], ")"]], InterpretTemplate[Function[List[$CellContext`e1, $CellContext`e2, $CellContext`e3], LerchPhi[$CellContext`e1, $CellContext`e2, $CellContext`e3]]]] </annotation> </semantics> <mrow> <mi> log </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mfrac> </mrow> <mo> ⩵ </mo> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <limit /> <bvar> <ci> z </ci> </bvar> <condition> <apply> <tendsto /> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> </condition> <apply> <times /> <apply> <ci> LerchPhi </ci> <ci> z </ci> <cn type='integer'> 1 </cn> <ci> a </ci> </apply> <apply> <power /> <apply> <ln /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </annotation-xml> </semantics> </math>
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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Limit", "[", RowBox[List[FractionBox[RowBox[List["LerchPhiClassical", "[", RowBox[List["z_", ",", "1", ",", "a_"]], "]"]], RowBox[List["Log", "[", RowBox[List["1", "-", "z_"]], "]"]]], ",", RowBox[List["z_", "\[Rule]", "1"]]]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List["-", "1"]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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