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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 hyperbolic functions > Involving exp and sinh





http://functions.wolfram.com/06.28.21.0095.01









  


  










Input Form





Integrate[E^(b z) Sinh[c z] Erfi[a z], z] == (E^((b - c)^2/(4 a^2)) ((b + c) E^((b c)/a^2) Erfi[(b - c + 2 a^2 z)/(2 a)] + (-b + c) Erfi[(b + c + 2 a^2 z)/(2 a)]) + 2 E^((b^2 + c^2 + 2 a^2 b z)/(2 a^2)) Erfi[a z] ((-c) Cosh[c z] + b Sinh[c z]))/(2 (b^2 - c^2))/E^((b^2 + c^2)/(2 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["\[ExponentialE]", RowBox[List["b_", " ", "z_"]]], " ", RowBox[List["Sinh", "[", RowBox[List["c_", " ", "z_"]], "]"]], " ", RowBox[List["Erfi", "[", RowBox[List["a_", " ", "z_"]], "]"]]]], RowBox[List["\[DifferentialD]", "z_"]]]]]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["-", FractionBox[RowBox[List[SuperscriptBox["b", "2"], "+", SuperscriptBox["c", "2"]]], RowBox[List["2", " ", SuperscriptBox["a", "2"]]]]]]], " ", RowBox[List["(", RowBox[List[RowBox[List[SuperscriptBox["\[ExponentialE]", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["b", "-", "c"]], ")"]], "2"], RowBox[List["4", " ", SuperscriptBox["a", "2"]]]]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List["b", "+", "c"]], ")"]], " ", SuperscriptBox["\[ExponentialE]", FractionBox[RowBox[List["b", " ", "c"]], SuperscriptBox["a", "2"]]], " ", RowBox[List["Erfi", "[", FractionBox[RowBox[List["b", "-", "c", "+", RowBox[List["2", " ", SuperscriptBox["a", "2"], " ", "z"]]]], RowBox[List["2", " ", "a"]]], "]"]]]], "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "b"]], "+", "c"]], ")"]], " ", RowBox[List["Erfi", "[", FractionBox[RowBox[List["b", "+", "c", "+", RowBox[List["2", " ", SuperscriptBox["a", "2"], " ", "z"]]]], RowBox[List["2", " ", "a"]]], "]"]]]]]], ")"]]]], "+", RowBox[List["2", " ", SuperscriptBox["\[ExponentialE]", FractionBox[RowBox[List[SuperscriptBox["b", "2"], "+", SuperscriptBox["c", "2"], "+", RowBox[List["2", " ", SuperscriptBox["a", "2"], " ", "b", " ", "z"]]]], RowBox[List["2", " ", SuperscriptBox["a", "2"]]]]], " ", RowBox[List["Erfi", "[", RowBox[List["a", " ", "z"]], "]"]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "c"]], " ", RowBox[List["Cosh", "[", RowBox[List["c", " ", "z"]], "]"]]]], "+", RowBox[List["b", " ", RowBox[List["Sinh", "[", RowBox[List["c", " ", "z"]], "]"]]]]]], ")"]]]]]], ")"]]]], RowBox[List["2", " ", RowBox[List["(", RowBox[List[SuperscriptBox["b", "2"], "-", SuperscriptBox["c", "2"]]], ")"]]]]]]]]]










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





2001-10-29