|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
http://functions.wolfram.com/05.15.02.0001.01
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
BellB[n, z] == n! SeriesTerm[E^((E^t - 1) z), {t, 0, n}] /;
Element[n, Integers] && n >= 0
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["BellB", "[", RowBox[List["n", ",", "z"]], "]"]], "\[Equal]", RowBox[List[RowBox[List["n", "!"]], RowBox[List["SeriesTerm", "[", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["(", RowBox[List[SuperscriptBox["\[ExponentialE]", "t"], "-", "1"]], ")"]], "z"]]], ",", RowBox[List["{", RowBox[List["t", ",", "0", ",", "n"]], "}"]]]], "]"]]]]]], "/;", RowBox[List[RowBox[List["n", "\[Element]", "Integers"]], "\[And]", RowBox[List["n", "\[GreaterEqual]", "0"]]]]]]]]
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <mrow> <msub> <semantics> <mi> B </mi> <annotation encoding='Mathematica'> TagBox["B", BellB] </annotation> </semantics> <mi> n </mi> </msub> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo>  </mo> <mrow> <mrow> <mi> n </mi> <mo> ! </mo> </mrow> <mo> ⁢ </mo> <mtext> </mtext> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> [ </mo> <msup> <mi> t </mi> <mi> n </mi> </msup> <mtext> </mtext> <mo> ] </mo> </mrow> <mo> ⁢ </mo> <msup> <mi> ⅇ </mi> <mrow> <mrow> <mo> ( </mo> <mrow> <msup> <mi> ⅇ </mi> <mi> t </mi> </msup> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mi> z </mi> </mrow> </msup> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> /; </mo> <mrow> <mi> n </mi> <mo> ∈ </mo> <semantics> <mi> ℕ </mi> <annotation encoding='Mathematica'> TagBox["\[DoubleStruckCapitalN]", Function[Integers]] </annotation> </semantics> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <mrow> <mrow> <mrow> <msub> <semantics> <mi> B </mi> <annotation encoding='Mathematica'> TagBox["B", BellB] </annotation> </semantics> <mi> n </mi> </msub> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo>  </mo> <mrow> <mrow> <mi> n </mi> <mo> ! </mo> </mrow> <mo> ⁢ </mo> <mtext> </mtext> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> [ </mo> <msup> <mi> t </mi> <mi> n </mi> </msup> <mtext> </mtext> <mo> ] </mo> </mrow> <mo> ⁢ </mo> <msup> <mi> ⅇ </mi> <mrow> <mrow> <mo> ( </mo> <mrow> <msup> <mi> ⅇ </mi> <mi> t </mi> </msup> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mi> z </mi> </mrow> </msup> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> /; </mo> <mrow> <mi> n </mi> <mo> ∈ </mo> <semantics> <mi> ℕ </mi> <annotation encoding='Mathematica'> TagBox["\[DoubleStruckCapitalN]", Function[Integers]] </annotation> </semantics> </mrow> </mrow> </annotation-xml> </semantics> </math>
|
|
|
|
|
|
|
|
|
|
| |
|
|
|
|
| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["BellB", "[", RowBox[List["n_", ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[RowBox[List["n", "!"]], " ", RowBox[List["SeriesTerm", "[", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["(", RowBox[List[SuperscriptBox["\[ExponentialE]", "t"], "-", "1"]], ")"]], " ", "z"]]], ",", RowBox[List["{", RowBox[List["t", ",", "0", ",", "n"]], "}"]]]], "]"]]]], "/;", RowBox[List[RowBox[List["n", "\[Element]", "Integers"]], "&&", RowBox[List["n", "\[GreaterEqual]", "0"]]]]]]]]]] |
|
|
|
|
|
|
|
|
|
|
|
Date Added to functions.wolfram.com (modification date)
|
|
|
|
|
|
|
|
|
|
|
|
|
 |
){kind=small}
