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http://functions.wolfram.com/02.05.09.0006.01
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E == 1 + Limit[z^z/HarmonicNumber[z - 1, -z], z -> Infinity]
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Cell[BoxData[RowBox[List["\[ExponentialE]", "\[Equal]", RowBox[List["1", "+", RowBox[List["Limit", "[", RowBox[List[FractionBox[SuperscriptBox["z", "z"], RowBox[List["HarmonicNumber", "[", RowBox[List[RowBox[List["z", "-", "1"]], ",", RowBox[List["-", "z"]]]], "]"]]], ",", RowBox[List["z", "\[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> <mi> ⅇ </mi> <mo> ⩵ </mo> <mrow> <mrow> <munder> <mi> lim </mi> <mrow> <mi> z </mi> <semantics> <mo> → </mo> <annotation encoding='Mathematica'> "\[Rule]" </annotation> </semantics> <mi> ∞ </mi> </mrow> </munder> <mo> ⁢ </mo> <mtext>   </mtext> <mfrac> <msup> <mi> z </mi> <mi> z </mi> </msup> <msubsup> <semantics> <mi> H </mi> <annotation-xml encoding='MathML-Content'> <ci> HarmonicNumber </ci> </annotation-xml> </semantics> <mrow> <mi> z </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </msubsup> </mfrac> </mrow> <mo> + </mo> <mn> 1 </mn> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <exponentiale /> <apply> <plus /> <apply> <limit /> <bvar> <ci> z </ci> </bvar> <condition> <apply> <tendsto /> <ci> z </ci> <infinity /> </apply> </condition> <apply> <times /> <apply> <power /> <ci> z </ci> <ci> z </ci> </apply> <apply> <power /> <apply> <ci> HarmonicNumber </ci> <apply> <plus /> <ci> z </ci> <cn type='integer'> -1 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <cn type='integer'> 1 </cn> </apply> </apply> </annotation-xml> </semantics> </math>
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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", "\[ExponentialE]", "]"]], "\[RuleDelayed]", RowBox[List["1", "+", RowBox[List["Limit", "[", RowBox[List[FractionBox[SuperscriptBox["z", "z"], RowBox[List["HarmonicNumber", "[", RowBox[List[RowBox[List["z", "-", "1"]], ",", RowBox[List["-", "z"]]]], "]"]]], ",", RowBox[List["z", "\[Rule]", "\[Infinity]"]]]], "]"]]]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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){kind=small}
