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; }

 Erf

 http://functions.wolfram.com/06.25.21.0088.01

 Input Form

 Integrate[z^2 Cosh[b z] Erf[a z], z] == ((1/(8 a^4 b^3 Sqrt[Pi])) (-8 a^3 b + 2 a b^3 - 8 a^3 b E^(2 b z) + 2 a b^3 E^(2 b z) - 4 a^3 b^2 z + 4 a^3 b^2 E^(2 b z) z + (8 a^4 - 2 a^2 b^2 + b^4) E^((b + 2 a^2 z)^2/(4 a^2)) Sqrt[Pi] Erf[b/(2 a) - a z] + 8 a^4 E^((b + 2 a^2 z)^2/(4 a^2)) Sqrt[Pi] Erf[b/(2 a) + a z] - 2 a^2 b^2 E^((b + 2 a^2 z)^2/(4 a^2)) Sqrt[Pi] Erf[b/(2 a) + a z] + b^4 E^((b + 2 a^2 z)^2/(4 a^2)) Sqrt[Pi] Erf[b/(2 a) + a z] - 8 a^4 E^(a^2 z^2) Sqrt[Pi] Erf[a z] (1 + b z + E^(2 b z) (-1 + b z) - b^2 E^(b z) z^2 Sinh[b z])))/ E^(z (b + a^2 z))

 Standard Form

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 MathML Form

 z 2 cosh ( b z ) erf ( a z ) z 1 8 a 4 b 3 π - z ( z a 2 + b ) ( 8 exp ( ( 2 z a 2 + b ) 2 4 a 2 ) π erf ( b 2 a + a z ) a 4 - 8 a 2 z 2 π erf ( a z ) ( - b 2 b z sinh ( b z ) z 2 + b z + 2 b z ( b z - 1 ) + 1 ) a 4 - 8 b 2 b z a 3 - 8 b a 3 + 4 b 2 2 b z z a 3 - 4 b 2 z a 3 - 2 b 2 ( 2 z a 2 + b ) 2 4 a 2 π erf ( b 2 a + a z ) a 2 + 2 b 3 2 b z a + 2 b 3 a + b 4 exp ( ( 2 z a 2 + b ) 2 4 a 2 ) π erf ( b 2 a + a z ) + ( 8 a 4 - 2 b 2 a 2 + b 4 ) ( 2 z a 2 + b ) 2 4 a 2 π erf ( b 2 a - a z ) ) z z 2 b z Erf a z 1 8 a 4 b 3 1 2 -1 -1 z z a 2 b 8 2 z a 2 b 2 4 a 2 -1 1 2 Erf b 2 a -1 a z a 4 -1 8 a 2 z 2 1 2 Erf a z -1 b 2 b z b z z 2 b z 2 b z b z -1 1 a 4 -1 8 b 2 b z a 3 -1 8 b a 3 4 b 2 2 b z z a 3 -1 4 b 2 z a 3 -1 2 b 2 2 z a 2 b 2 4 a 2 -1 1 2 Erf b 2 a -1 a z a 2 2 b 3 2 b z a 2 b 3 a b 4 2 z a 2 b 2 4 a 2 -1 1 2 Erf b 2 a -1 a z 8 a 4 -1 2 b 2 a 2 b 4 2 z a 2 b 2 4 a 2 -1 1 2 Erf b 2 a -1 -1 a z [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["\[Integral]", RowBox[List[RowBox[List[SuperscriptBox["z_", "2"], " ", RowBox[List["Cosh", "[", RowBox[List["b_", " ", "z_"]], "]"]], " ", RowBox[List["Erf", "[", RowBox[List["a_", " ", "z_"]], "]"]]]], RowBox[List["\[DifferentialD]", "z_"]]]]]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["-", "z"]], " ", RowBox[List["(", RowBox[List["b", "+", RowBox[List[SuperscriptBox["a", "2"], " ", "z"]]]], ")"]]]]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "8"]], " ", SuperscriptBox["a", "3"], " ", "b"]], "+", RowBox[List["2", " ", "a", " ", SuperscriptBox["b", "3"]]], "-", RowBox[List["8", " ", SuperscriptBox["a", "3"], " ", "b", " ", SuperscriptBox["\[ExponentialE]", RowBox[List["2", " ", "b", " ", "z"]]]]], "+", RowBox[List["2", " ", "a", " ", SuperscriptBox["b", "3"], " ", SuperscriptBox["\[ExponentialE]", RowBox[List["2", " ", "b", " ", "z"]]]]], "-", RowBox[List["4", " ", SuperscriptBox["a", "3"], " ", SuperscriptBox["b", "2"], " ", "z"]], "+", RowBox[List["4", " ", SuperscriptBox["a", "3"], " ", SuperscriptBox["b", "2"], " ", SuperscriptBox["\[ExponentialE]", RowBox[List["2", " ", "b", " ", "z"]]], " ", "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"]]], ")"]], " ", SuperscriptBox["\[ExponentialE]", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["b", "+", RowBox[List["2", " ", SuperscriptBox["a", "2"], " ", "z"]]]], ")"]], "2"], RowBox[List["4", " ", SuperscriptBox["a", "2"]]]]], " ", SqrtBox["\[Pi]"], " ", RowBox[List["Erf", "[", RowBox[List[FractionBox["b", RowBox[List["2", " ", "a"]]], "-", RowBox[List["a", " ", "z"]]]], "]"]]]], "+", RowBox[List["8", " ", SuperscriptBox["a", "4"], " ", SuperscriptBox["\[ExponentialE]", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["b", "+", RowBox[List["2", " ", SuperscriptBox["a", "2"], " ", "z"]]]], ")"]], "2"], RowBox[List["4", " ", SuperscriptBox["a", "2"]]]]], " ", SqrtBox["\[Pi]"], " ", RowBox[List["Erf", "[", RowBox[List[FractionBox["b", RowBox[List["2", " ", "a"]]], "+", RowBox[List["a", " ", "z"]]]], "]"]]]], "-", RowBox[List["2", " ", SuperscriptBox["a", "2"], " ", SuperscriptBox["b", "2"], " ", SuperscriptBox["\[ExponentialE]", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["b", "+", RowBox[List["2", " ", SuperscriptBox["a", "2"], " ", "z"]]]], ")"]], "2"], RowBox[List["4", " ", SuperscriptBox["a", "2"]]]]], " ", SqrtBox["\[Pi]"], " ", RowBox[List["Erf", "[", RowBox[List[FractionBox["b", RowBox[List["2", " ", "a"]]], "+", RowBox[List["a", " ", "z"]]]], "]"]]]], "+", RowBox[List[SuperscriptBox["b", "4"], " ", SuperscriptBox["\[ExponentialE]", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["b", "+", RowBox[List["2", " ", SuperscriptBox["a", "2"], " ", "z"]]]], ")"]], "2"], RowBox[List["4", " ", SuperscriptBox["a", "2"]]]]], " ", SqrtBox["\[Pi]"], " ", RowBox[List["Erf", "[", RowBox[List[FractionBox["b", RowBox[List["2", " ", "a"]]], "+", RowBox[List["a", " ", "z"]]]], "]"]]]], "-", RowBox[List["8", " ", SuperscriptBox["a", "4"], " ", SuperscriptBox["\[ExponentialE]", RowBox[List[SuperscriptBox["a", "2"], " ", SuperscriptBox["z", "2"]]]], " ", SqrtBox["\[Pi]"], " ", RowBox[List["Erf", "[", RowBox[List["a", " ", "z"]], "]"]], " ", RowBox[List["(", RowBox[List["1", "+", RowBox[List["b", " ", "z"]], "+", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["2", " ", "b", " ", "z"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", RowBox[List["b", " ", "z"]]]], ")"]]]], "-", RowBox[List[SuperscriptBox["b", "2"], " ", SuperscriptBox["\[ExponentialE]", RowBox[List["b", " ", "z"]]], " ", SuperscriptBox["z", "2"], " ", RowBox[List["Sinh", "[", RowBox[List["b", " ", "z"]], "]"]]]]]], ")"]]]]]], ")"]]]], RowBox[List["8", " ", SuperscriptBox["a", "4"], " ", SuperscriptBox["b", "3"], " ", SqrtBox["\[Pi]"]]]]]]]]

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

 2001-10-29