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variants of this functions
Erf






Mathematica Notation

Traditional Notation









Gamma, Beta, Erf > Erf[z] > Integration > Indefinite integration > Involving one direct function and elementary functions > Involving exponential function and a power function > Involving exp and power





http://functions.wolfram.com/06.25.21.0025.01









  


  










Input Form





Integrate[z^3 E^(b z^2) Erf[a z], z] == (1/(2 b^2)) (E^(b z^2) (-1 + b z^2) Erf[a z] + (a b z^3 (Sqrt[Pi] + 2 E^((-a^2 + b) z^2) Sqrt[(a^2 - b) z^2] - Sqrt[Pi] Erf[Sqrt[(a^2 - b) z^2]]))/ (2 Sqrt[Pi] ((a^2 - b) z^2)^(3/2)) + (a Erfi[Sqrt[-a^2 + b] z])/ Sqrt[-a^2 + b])










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["\[ExponentialE]", RowBox[List["b_", " ", SuperscriptBox["z_", "2"]]]], " ", RowBox[List["Erf", "[", RowBox[List["a_", " ", "z_"]], "]"]]]], RowBox[List["\[DifferentialD]", "z_"]]]]]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["b", " ", SuperscriptBox["z", "2"]]]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", RowBox[List["b", " ", SuperscriptBox["z", "2"]]]]], ")"]], " ", RowBox[List["Erf", "[", RowBox[List["a", " ", "z"]], "]"]]]], "+", FractionBox[RowBox[List["a", " ", "b", " ", SuperscriptBox["z", "3"], " ", RowBox[List["(", RowBox[List[SqrtBox["\[Pi]"], "+", RowBox[List["2", " ", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", SuperscriptBox["a", "2"]]], "+", "b"]], ")"]], " ", SuperscriptBox["z", "2"]]]], " ", SqrtBox[RowBox[List[RowBox[List["(", RowBox[List[SuperscriptBox["a", "2"], "-", "b"]], ")"]], " ", SuperscriptBox["z", "2"]]]]]], "-", RowBox[List[SqrtBox["\[Pi]"], " ", RowBox[List["Erf", "[", SqrtBox[RowBox[List[RowBox[List["(", RowBox[List[SuperscriptBox["a", "2"], "-", "b"]], ")"]], " ", SuperscriptBox["z", "2"]]]], "]"]]]]]], ")"]]]], RowBox[List["2", " ", SqrtBox["\[Pi]"], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List[SuperscriptBox["a", "2"], "-", "b"]], ")"]], " ", SuperscriptBox["z", "2"]]], ")"]], RowBox[List["3", "/", "2"]]]]]], "+", FractionBox[RowBox[List["a", " ", RowBox[List["Erfi", "[", RowBox[List[SqrtBox[RowBox[List[RowBox[List["-", SuperscriptBox["a", "2"]]], "+", "b"]]], " ", "z"]], "]"]]]], SqrtBox[RowBox[List[RowBox[List["-", SuperscriptBox["a", "2"]]], "+", "b"]]]]]], RowBox[List["2", " ", SuperscriptBox["b", "2"]]]]]]]]










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





2001-10-29





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