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Erfc






Mathematica Notation

Traditional Notation









Gamma, Beta, Erf > Erfc[z] > Integration > Indefinite integration > Involving functions of the direct function and elementary functions > Involving elementary functions of the direct function and elementary functions > Involving powers of the direct function and a power function





http://functions.wolfram.com/06.27.21.0124.01









  


  










Input Form





Integrate[z^3 Erfc[a z]^2, z] == (1/(16 a^4 Pi)) ((8 + 4 a^2 z^2 - 4 a E^(a^2 z^2) Sqrt[Pi] z (3 + 2 a^2 z^2) Erfc[a z] + E^(2 a^2 z^2) Pi (3 + (-3 + 4 a^4 z^4) Erfc[a z]^2))/E^(2 a^2 z^2))










Standard Form





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MathML Form







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Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["\[Integral]", RowBox[List[RowBox[List[SuperscriptBox["z_", "3"], " ", SuperscriptBox[RowBox[List["Erfc", "[", RowBox[List["a_", " ", "z_"]], "]"]], "2"]]], RowBox[List["\[DifferentialD]", "z_"]]]]]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["-", "2"]], " ", SuperscriptBox["a", "2"], " ", SuperscriptBox["z", "2"]]]], " ", RowBox[List["(", RowBox[List["8", "+", RowBox[List["4", " ", SuperscriptBox["a", "2"], " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["4", " ", "a", " ", SuperscriptBox["\[ExponentialE]", RowBox[List[SuperscriptBox["a", "2"], " ", SuperscriptBox["z", "2"]]]], " ", SqrtBox["\[Pi]"], " ", "z", " ", RowBox[List["(", RowBox[List["3", "+", RowBox[List["2", " ", SuperscriptBox["a", "2"], " ", SuperscriptBox["z", "2"]]]]], ")"]], " ", RowBox[List["Erfc", "[", RowBox[List["a", " ", "z"]], "]"]]]], "+", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["2", " ", SuperscriptBox["a", "2"], " ", SuperscriptBox["z", "2"]]]], " ", "\[Pi]", " ", RowBox[List["(", RowBox[List["3", "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "3"]], "+", RowBox[List["4", " ", SuperscriptBox["a", "4"], " ", SuperscriptBox["z", "4"]]]]], ")"]], " ", SuperscriptBox[RowBox[List["Erfc", "[", RowBox[List["a", " ", "z"]], "]"]], "2"]]]]], ")"]]]]]], ")"]]]], RowBox[List["16", " ", SuperscriptBox["a", "4"], " ", "\[Pi]"]]]]]]]










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





2001-10-29