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Erfi






Mathematica Notation

Traditional Notation









Gamma, Beta, Erf > Erfi[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/06.28.21.0018.01









  


  










Input Form





Integrate[z^2 E^(b z) Erfi[a z], z] == (1/(4 a^4 b^3 Sqrt[Pi])) ((-2 a b E^((b + 2 a^2 z)^2/(4 a^2)) (-b^2 + 2 a^2 (-2 + b z)) + Sqrt[Pi] (4 a^4 E^(b^2/(4 a^2) + b z) (2 + b z (-2 + b z)) Erfi[a z] - (8 a^4 + 2 a^2 b^2 + b^4) Erfi[b/(2 a) + a z]))/E^(b^2/(4 a^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_", "2"], " ", SuperscriptBox["\[ExponentialE]", RowBox[List["b_", " ", "z_"]]], " ", RowBox[List["Erfi", "[", RowBox[List["a_", " ", "z_"]], "]"]]]], RowBox[List["\[DifferentialD]", "z_"]]]]]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["-", FractionBox[SuperscriptBox["b", "2"], RowBox[List["4", " ", SuperscriptBox["a", "2"]]]]]]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "a", " ", "b", " ", SuperscriptBox["\[ExponentialE]", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["b", "+", RowBox[List["2", " ", SuperscriptBox["a", "2"], " ", "z"]]]], ")"]], "2"], RowBox[List["4", " ", SuperscriptBox["a", "2"]]]]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", SuperscriptBox["b", "2"]]], "+", RowBox[List["2", " ", SuperscriptBox["a", "2"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "2"]], "+", RowBox[List["b", " ", "z"]]]], ")"]]]]]], ")"]]]], "+", RowBox[List[SqrtBox["\[Pi]"], " ", RowBox[List["(", RowBox[List[RowBox[List["4", " ", SuperscriptBox["a", "4"], " ", SuperscriptBox["\[ExponentialE]", RowBox[List[FractionBox[SuperscriptBox["b", "2"], RowBox[List["4", " ", SuperscriptBox["a", "2"]]]], "+", RowBox[List["b", " ", "z"]]]]], " ", RowBox[List["(", RowBox[List["2", "+", RowBox[List["b", " ", "z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "2"]], "+", RowBox[List["b", " ", "z"]]]], ")"]]]]]], ")"]], " ", RowBox[List["Erfi", "[", RowBox[List["a", " ", "z"]], "]"]]]], "-", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["8", " ", SuperscriptBox["a", "4"]]], "+", RowBox[List["2", " ", SuperscriptBox["a", "2"], " ", SuperscriptBox["b", "2"]]], "+", SuperscriptBox["b", "4"]]], ")"]], " ", RowBox[List["Erfi", "[", RowBox[List[FractionBox["b", RowBox[List["2", " ", "a"]]], "+", RowBox[List["a", " ", "z"]]]], "]"]]]]]], ")"]]]]]], ")"]]]], RowBox[List["4", " ", SuperscriptBox["a", "4"], " ", SuperscriptBox["b", "3"], " ", SqrtBox["\[Pi]"]]]]]]]]










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





2001-10-29





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