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http://functions.wolfram.com/01.03.09.0003.01
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E^z == Limit[((2 n + z)/(2 n - z))^n, n -> Infinity]
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Cell[BoxData[RowBox[List[SuperscriptBox["\[ExponentialE]", "z"], "\[Equal]", RowBox[List["Limit", "[", RowBox[List[SuperscriptBox[RowBox[List["(", FractionBox[RowBox[List[RowBox[List["2", " ", "n"]], "+", "z"]], RowBox[List[RowBox[List["2", " ", "n"]], "-", "z"]]], ")"]], "n"], ",", RowBox[List["n", "\[Rule]", "\[Infinity]"]]]], "]"]]]]]]
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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> <msup> <mi> ⅇ </mi> <mi> z </mi> </msup> <mo> ⩵ </mo> <mrow> <munder> <mi> lim </mi> <mrow> <mi> n </mi> <semantics> <mo> → </mo> <annotation encoding='Mathematica'> "\[Rule]" </annotation> </semantics> <mi> ∞ </mi> </mrow> </munder> <mo> ⁢ </mo> <mtext>   </mtext> <msup> <mrow> <mo> ( </mo> <mfrac> <mrow> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> n </mi> </mrow> <mo> + </mo> <mi> z </mi> </mrow> <mrow> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> n </mi> </mrow> <mo> - </mo> <mi> z </mi> </mrow> </mfrac> <mo> ) </mo> </mrow> <mi> n </mi> </msup> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <power /> <exponentiale /> <ci> z </ci> </apply> <apply> <limit /> <bvar> <ci> n </ci> </bvar> <condition> <apply> <tendsto /> <ci> n </ci> <infinity /> </apply> </condition> <apply> <power /> <apply> <times /> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> n </ci> </apply> <ci> z </ci> </apply> <apply> <power /> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> n </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <ci> n </ci> </apply> </apply> </apply> </annotation-xml> </semantics> </math>
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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", SuperscriptBox["\[ExponentialE]", "z_"], "]"]], "\[RuleDelayed]", RowBox[List["Limit", "[", RowBox[List[SuperscriptBox[RowBox[List["(", FractionBox[RowBox[List[RowBox[List["2", " ", "n"]], "+", "z"]], RowBox[List[RowBox[List["2", " ", "n"]], "-", "z"]]], ")"]], "n"], ",", RowBox[List["n", "\[Rule]", "\[Infinity]"]]]], "]"]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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){kind=small}
