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http://functions.wolfram.com/04.23.23.0002.01
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Sum[(BellB[n]/n!) z^n, {n, 0, Infinity}] == E^(E^z - 1)
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Cell[BoxData[RowBox[List[RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["n", "=", "0"]], "\[Infinity]"], RowBox[List[FractionBox[RowBox[List["BellB", "[", "n", "]"]], RowBox[List["n", "!"]]], " ", SuperscriptBox["z", "n"]]]]], "\[Equal]", SuperscriptBox["\[ExponentialE]", RowBox[List[SuperscriptBox["\[ExponentialE]", "z"], "-", "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> <munderover> <mo> ∑ </mo> <mrow> <mi> n </mi> <mo> = </mo> <mn> 0 </mn> </mrow> <mi> ∞ </mi> </munderover> <mfrac> <mrow> <msub> <semantics> <mi> B </mi> <annotation encoding='Mathematica'> TagBox["B", BellB] </annotation> </semantics> <mi> n </mi> </msub> <mo> ⁢ </mo> <msup> <mi> z </mi> <mi> n </mi> </msup> </mrow> <mrow> <mi> n </mi> <mo> ! </mo> </mrow> </mfrac> </mrow> <mo>  </mo> <msup> <mi> ⅇ </mi> <mrow> <msup> <mi> ⅇ </mi> <mi> z </mi> </msup> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <sum /> <bvar> <ci> n </ci> </bvar> <lowlimit> <cn type='integer'> 0 </cn> </lowlimit> <uplimit> <infinity /> </uplimit> <apply> <times /> <apply> <ci> BellB </ci> <ci> n </ci> </apply> <apply> <power /> <ci> z </ci> <ci> n </ci> </apply> <apply> <power /> <apply> <factorial /> <ci> n </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <power /> <exponentiale /> <apply> <plus /> <apply> <power /> <exponentiale /> <ci> z </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </annotation-xml> </semantics> </math>
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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["n_", "=", "0"]], "\[Infinity]"], FractionBox[RowBox[List[RowBox[List["BellB", "[", "n_", "]"]], " ", SuperscriptBox["z_", "n_"]]], RowBox[List["n_", "!"]]]]], "]"]], "\[RuleDelayed]", SuperscriptBox["\[ExponentialE]", RowBox[List[SuperscriptBox["\[ExponentialE]", "z"], "-", "1"]]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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){kind=small}
