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 StirlingS1

 http://functions.wolfram.com/04.14.03.0047.01

 Input Form

 StirlingS1[m + 1, m] == (-(1/2)) m (1 + m) /; Element[m, Integers] && m >= 0

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["StirlingS1", "[", RowBox[List[RowBox[List["m", "+", "1"]], ",", "m"]], "]"]], "\[Equal]", RowBox[List[RowBox[List["-", FractionBox["1", "2"]]], " ", "m", " ", RowBox[List["(", RowBox[List["1", "+", "m"]], ")"]]]]]], "/;", RowBox[List[RowBox[List["m", "\[Element]", "Integers"]], "\[And]", RowBox[List["m", "\[GreaterEqual]", "0"]]]]]]]]

 MathML Form

 S TagBox["S", StirlingS1] m + 1 ( m ) - 1 2 m ( m + 1 ) /; m TagBox["\[DoubleStruckCapitalN]", Function[Integers]] Condition StirlingS1 m 1 m -1 1 2 m m 1 m [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["StirlingS1", "[", RowBox[List[RowBox[List["m_", "+", "1"]], ",", "m_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[RowBox[List["-", FractionBox["1", "2"]]], " ", "m", " ", RowBox[List["(", RowBox[List["1", "+", "m"]], ")"]]]], "/;", RowBox[List[RowBox[List["m", "\[Element]", "Integers"]], "&&", RowBox[List["m", "\[GreaterEqual]", "0"]]]]]]]]]]

 Date Added to functions.wolfram.com (modification date)

 2007-05-02