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   http://functions.wolfram.com/02.05.09.0008.01
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    E == (1 + s)^(1/s) Limit[(Sum[k^s, {k, 1, n}]/
      (n Product[k^s, {k, 1, n}]^(1/n)))^(1/s), n -> Infinity] /; s > 0 
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   Cell[BoxData[RowBox[List[RowBox[List["\[ExponentialE]", "\[Equal]", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", "s"]], ")"]], FractionBox["1", "s"]], RowBox[List["Limit", "[", RowBox[List[SuperscriptBox[RowBox[List["(", FractionBox[RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "1"]], "n"], SuperscriptBox["k", "s"]]], RowBox[List["n", SuperscriptBox[RowBox[List["(", RowBox[List[UnderoverscriptBox["\[Product]", RowBox[List["k", "=", "1"]], "n"], SuperscriptBox["k", "s"]]], ")"]], FractionBox["1", "n"]]]]], ")"]], FractionBox["1", "s"]], ",", RowBox[List["n", "\[Rule]", "\[Infinity]"]]]], "]"]]]]]], "/;", "\[InvisibleSpace]", RowBox[List["s", ">", "0"]]]]]] 
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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>  <mi> ⅇ </mi>  <mo> ⩵ </mo>  <mrow>  <msup>  <mrow>  <mo> ( </mo>  <mrow>  <mi> s </mi>  <mo> + </mo>  <mn> 1 </mn>  </mrow>  <mo> ) </mo>  </mrow>  <mrow>  <mn> 1 </mn>  <mo> / </mo>  <mi> s </mi>  </mrow>  </msup>  <mo> ⁢ </mo>  <mrow>  <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>  <munderover>  <mo> ∑ </mo>  <mrow>  <mi> k </mi>  <mo> = </mo>  <mn> 1 </mn>  </mrow>  <mi> n </mi>  </munderover>  <msup>  <mi> k </mi>  <mi> s </mi>  </msup>  </mrow>  <mrow>  <mi> n </mi>  <mo> ⁢ </mo>  <msup>  <mrow>  <mo> ( </mo>  <mrow>  <munderover>  <mo> ∏ </mo>  <mrow>  <mi> k </mi>  <mo> = </mo>  <mn> 1 </mn>  </mrow>  <mi> n </mi>  </munderover>  <msup>  <mi> k </mi>  <mi> s </mi>  </msup>  </mrow>  <mo> ) </mo>  </mrow>  <mrow>  <mn> 1 </mn>  <mo> / </mo>  <mi> n </mi>  </mrow>  </msup>  </mrow>  </mfrac>  <mo> ) </mo>  </mrow>  <mrow>  <mn> 1 </mn>  <mo> / </mo>  <mi> s </mi>  </mrow>  </msup>  </mrow>  <mo> ) </mo>  </mrow>  </mrow>  </mrow>  <mo> /; </mo>  <mtext> ​ </mtext>  <mrow>  <mi> s </mi>  <mo> > </mo>  <mn> 0 </mn>  </mrow>  </mrow>  <annotation-xml encoding='MathML-Content'>  <apply>  <ci> Condition </ci>  <apply>  <eq />  <exponentiale />  <apply>  <times />  <apply>  <power />  <apply>  <plus />  <ci> s </ci>  <cn type='integer'> 1 </cn>  </apply>  <apply>  <times />  <cn type='integer'> 1 </cn>  <apply>  <power />  <ci> s </ci>  <cn type='integer'> -1 </cn>  </apply>  </apply>  </apply>  <apply>  <limit />  <bvar>  <ci> n </ci>  </bvar>  <condition>  <apply>  <tendsto />  <ci> n </ci>  <infinity />  </apply>  </condition>  <apply>  <power />  <apply>  <times />  <apply>  <sum />  <bvar>  <ci> k </ci>  </bvar>  <lowlimit>  <cn type='integer'> 1 </cn>  </lowlimit>  <uplimit>  <ci> n </ci>  </uplimit>  <apply>  <power />  <ci> k </ci>  <ci> s </ci>  </apply>  </apply>  <apply>  <power />  <apply>  <times />  <ci> n </ci>  <apply>  <power />  <apply>  <product />  <bvar>  <ci> k </ci>  </bvar>  <lowlimit>  <cn type='integer'> 1 </cn>  </lowlimit>  <uplimit>  <ci> n </ci>  </uplimit>  <apply>  <power />  <ci> k </ci>  <ci> s </ci>  </apply>  </apply>  <apply>  <times />  <cn type='integer'> 1 </cn>  <apply>  <power />  <ci> n </ci>  <cn type='integer'> -1 </cn>  </apply>  </apply>  </apply>  </apply>  <cn type='integer'> -1 </cn>  </apply>  </apply>  <apply>  <times />  <cn type='integer'> 1 </cn>  <apply>  <power />  <ci> s </ci>  <cn type='integer'> -1 </cn>  </apply>  </apply>  </apply>  </apply>  </apply>  </apply>  <apply>  <gt />  <ci> s </ci>  <cn type='integer'> 0 </cn>  </apply>  </apply>  </annotation-xml>  </semantics>  </math> 
   
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   Date Added to functions.wolfram.com (modification date)
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