html, body, form { margin: 0; padding: 0; width: 100%; } #calculate { position: relative; width: 177px; height: 110px; background: transparent url(/images/alphabox/embed_functions_inside.gif) no-repeat scroll 0 0; } #i { position: relative; left: 18px; top: 44px; width: 133px; border: 0 none; outline: 0; font-size: 11px; } #eq { width: 9px; height: 10px; background: transparent; position: absolute; top: 47px; right: 18px; cursor: pointer; }

 Erfi

 http://functions.wolfram.com/06.28.21.0037.01

 Input Form

 Integrate[z Sin[b z^2] Erfi[c + a z], z] == (1/(4 b (a^4 + b^2))) ((-2 (a^4 + b^2) E^((2 a^4 c^2)/(a^4 + b^2)) Cos[b z^2] Erfi[c + a z] + a Sqrt[a^2 - I b] (a^2 + I b) E^((1 + a^2/(a^2 + I b)) c^2) Erfi[(a c + a^2 z - I b z)/Sqrt[a^2 - I b]] + a (a^2 - I b) Sqrt[a^2 + I b] E^((1 + a^2/(a^2 - I b)) c^2) Erfi[(a c + a^2 z + I b z)/Sqrt[a^2 + I b]])/E^((2 a^4 c^2)/(a^4 + b^2)))

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List["\[Integral]", RowBox[List["z", " ", RowBox[List["Sin", "[", RowBox[List["b", " ", SuperscriptBox["z", "2"]]], "]"]], RowBox[List["Erfi", "[", RowBox[List["c", "+", RowBox[List["a", " ", "z"]]]], "]"]], RowBox[List["\[DifferentialD]", "z"]]]]]], "\[Equal]", RowBox[List[FractionBox["1", RowBox[List["4", " ", "b", " ", RowBox[List["(", RowBox[List[SuperscriptBox["a", "4"], "+", SuperscriptBox["b", "2"]]], ")"]]]]], RowBox[List["(", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["-", FractionBox[RowBox[List["2", " ", SuperscriptBox["a", "4"], " ", SuperscriptBox["c", "2"]]], RowBox[List[SuperscriptBox["a", "4"], "+", SuperscriptBox["b", "2"]]]]]]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", RowBox[List["(", RowBox[List[SuperscriptBox["a", "4"], "+", SuperscriptBox["b", "2"]]], ")"]], " ", SuperscriptBox["\[ExponentialE]", FractionBox[RowBox[List["2", " ", SuperscriptBox["a", "4"], " ", SuperscriptBox["c", "2"]]], RowBox[List[SuperscriptBox["a", "4"], "+", SuperscriptBox["b", "2"]]]]], " ", RowBox[List["Cos", "[", RowBox[List["b", " ", SuperscriptBox["z", "2"]]], "]"]], " ", RowBox[List["Erfi", "[", RowBox[List["c", "+", RowBox[List["a", " ", "z"]]]], "]"]]]], "+", RowBox[List["a", " ", SqrtBox[RowBox[List[SuperscriptBox["a", "2"], "-", RowBox[List["\[ImaginaryI]", " ", "b"]]]]], " ", RowBox[List["(", RowBox[List[SuperscriptBox["a", "2"], "+", RowBox[List["\[ImaginaryI]", " ", "b"]]]], ")"]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["(", RowBox[List["1", "+", FractionBox[SuperscriptBox["a", "2"], RowBox[List[SuperscriptBox["a", "2"], "+", RowBox[List["\[ImaginaryI]", " ", "b"]]]]]]], ")"]], " ", SuperscriptBox["c", "2"]]]], " ", RowBox[List["Erfi", "[", FractionBox[RowBox[List[RowBox[List["a", " ", "c"]], "+", RowBox[List[SuperscriptBox["a", "2"], " ", "z"]], "-", RowBox[List["\[ImaginaryI]", " ", "b", " ", "z"]]]], SqrtBox[RowBox[List[SuperscriptBox["a", "2"], "-", RowBox[List["\[ImaginaryI]", " ", "b"]]]]]], "]"]]]], "+", RowBox[List["a", " ", RowBox[List["(", RowBox[List[SuperscriptBox["a", "2"], "-", RowBox[List["\[ImaginaryI]", " ", "b"]]]], ")"]], " ", SqrtBox[RowBox[List[SuperscriptBox["a", "2"], "+", RowBox[List["\[ImaginaryI]", " ", "b"]]]]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["(", RowBox[List["1", "+", FractionBox[SuperscriptBox["a", "2"], RowBox[List[SuperscriptBox["a", "2"], "-", RowBox[List["\[ImaginaryI]", " ", "b"]]]]]]], ")"]], " ", SuperscriptBox["c", "2"]]]], " ", RowBox[List["Erfi", "[", FractionBox[RowBox[List[RowBox[List["a", " ", "c"]], "+", RowBox[List[SuperscriptBox["a", "2"], " ", "z"]], "+", RowBox[List["\[ImaginaryI]", " ", "b", " ", "z"]]]], SqrtBox[RowBox[List[SuperscriptBox["a", "2"], "+", RowBox[List["\[ImaginaryI]", " ", "b"]]]]]], "]"]]]]]], ")"]]]], ")"]]]]]]]]

 MathML Form

 z sin ( b z 2 ) erfi ( c + a z ) z 1 4 b ( a 4 + b 2 ) ( exp ( - 2 a 4 c 2 a 4 + b 2 ) ( a a 2 + b ( a 2 - b ) exp ( ( a 2 a 2 - b + 1 ) c 2 ) erfi ( z a 2 + c a + b z a 2 + b ) + a ( a 2 + b ) a 2 - b exp ( ( a 2 a 2 + b + 1 ) c 2 ) erfi ( z a 2 + c a - b z a 2 - b ) - 2 ( a 4 + b 2 ) 2 a 4 c 2 a 4 + b 2 cos ( b z 2 ) erfi ( c + a z ) ) ) z z b z 2 Erfi c a z 1 4 b a 4 b 2 -1 -1 2 a 4 c 2 a 4 b 2 -1 a a 2 b 1 2 a 2 -1 b a 2 a 2 -1 b -1 1 c 2 Erfi z a 2 c a b z a 2 b 1 2 -1 a a 2 b a 2 -1 b 1 2 a 2 a 2 b -1 1 c 2 Erfi z a 2 c a -1 b z a 2 -1 b 1 2 -1 -1 2 a 4 b 2 2 a 4 c 2 a 4 b 2 -1 b z 2 Erfi c a z [/itex]

 Rule Form

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

 2001-10-29