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Exp




Mathematica Notation

Traditional Notation









Elementary Functions > Exp[z] > Representations through more general functions > Through Meijer G > Classical cases for the direct function itself





http://functions.wolfram.com/01.03.26.0104.01









  


  








Input Form





E^(-z^(1/n)) == Sqrt[n] (2 Pi)^((1/2) (1 - n)) MeijerG[{{}, {}}, {{0, 1/n, 2/n, \[Ellipsis], (n - 1)/n}, {}}, z/n^n] /; Element[n, Integers] && n > 0








Standard Form





Cell[BoxData[RowBox[List[RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["-", SuperscriptBox["z", FractionBox["1", "n"]]]]], " ", "\[Equal]", RowBox[List[SqrtBox[RowBox[List["n", " "]]], SuperscriptBox[RowBox[List["(", RowBox[List["2", " ", "\[Pi]"]], ")"]], RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List["1", "-", "n"]], ")"]]]]], RowBox[List["MeijerG", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", "}"]], ",", RowBox[List["{", "}"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List["0", ",", FractionBox["1", "n"], ",", FractionBox["2", "n"], ",", "\[Ellipsis]", ",", FractionBox[RowBox[List["n", "-", "1"]], "n"]]], "}"]], ",", RowBox[List["{", "}"]]]], "}"]], ",", FractionBox["z", SuperscriptBox["n", "n"]]]], "]"]]]]]], "/;", RowBox[List[RowBox[List["n", "\[Element]", "Integers"]], "\[And]", RowBox[List["n", ">", "0"]]]]]]]]








MathML Form







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Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", SuperscriptBox["\[ExponentialE]", RowBox[List["-", SuperscriptBox["z_", FractionBox["1", "n_"]]]]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[SqrtBox["n"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["2", " ", "\[Pi]"]], ")"]], FractionBox[RowBox[List["1", "-", "n"]], "2"]], " ", RowBox[List["MeijerG", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", "}"]], ",", RowBox[List["{", "}"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List["0", ",", FractionBox["1", "n"], ",", FractionBox["2", "n"], ",", "\[Ellipsis]", ",", FractionBox[RowBox[List["n", "-", "1"]], "n"]]], "}"]], ",", RowBox[List["{", "}"]]]], "}"]], ",", FractionBox["z", SuperscriptBox["n", "n"]]]], "]"]]]], "/;", RowBox[List[RowBox[List["n", "\[Element]", "Integers"]], "&&", RowBox[List["n", ">", "0"]]]]]]]]]]


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





2003-08-21