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http://functions.wolfram.com/10.06.25.0001.01
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Limit[(1 - z)^(1 - s) LerchPhiClassical[z, s, a], z -> 1] == Gamma[1 - s] /;
Re s < 1
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Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["Limit", "[", RowBox[List[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["1", "-", "s"]]], " ", RowBox[List["LerchPhiClassical", "[", RowBox[List["z", ",", "s", ",", "a"]], "]"]]]], ",", RowBox[List["z", "\[Rule]", "1"]]]], "]"]], "\[Equal]", RowBox[List["Gamma", "[", RowBox[List["1", "-", "s"]], "]"]]]], "/;", RowBox[List[RowBox[List["Re", " ", "s"]], "<", "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> <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> <mrow> <msup> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> s </mi> </mrow> </msup> <mo> ⁢ </mo> <semantics> <mrow> <mover> <mi> Φ </mi> <mo> ^ </mo> </mover> <mo> ( </mo> <mrow> <mi> z </mi> <mo> , </mo> <mi> s </mi> <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["s", 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> </mrow> <mo> ⩵ </mo> <mrow> <mi> Γ </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> s </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> /; </mo> <mrow> <mrow> <mi> Re </mi> <mo> ⁢ </mo> <mi> s </mi> </mrow> <mo> < </mo> <mn> 1 </mn> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <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> <power /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> </apply> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> s </ci> </apply> </apply> </apply> <apply> <ci> LerchPhi </ci> <ci> z </ci> <ci> s </ci> <ci> a </ci> </apply> </apply> </apply> <apply> <ci> Gamma </ci> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> s </ci> </apply> </apply> </apply> </apply> <apply> <lt /> <apply> <times /> <real /> <ci> s </ci> </apply> <cn type='integer'> 1 </cn> </apply> </apply> </annotation-xml> </semantics> </math>
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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Limit", "[", RowBox[List[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z_"]], ")"]], RowBox[List["1", "-", "s_"]]], " ", RowBox[List["LerchPhiClassical", "[", RowBox[List["z_", ",", "s_", ",", "a_"]], "]"]]]], ",", RowBox[List["z_", "\[Rule]", "1"]]]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["Gamma", "[", RowBox[List["1", "-", "s"]], "]"]], "/;", RowBox[List[RowBox[List["Re", " ", "s"]], "<", "1"]]]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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