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; }

 Exp

 http://functions.wolfram.com/01.03.21.0375.01

 Input Form

 Integrate[E^(b Sqrt[z] + d z) (E^(Sqrt[z] c + f z + g))^\[Nu], z] == (1/(2 (d + f \[Nu])^(3/2))) (E^(b Sqrt[z] + d z - (b + 2 d Sqrt[z] + (c + 2 f Sqrt[z]) \[Nu])^2/ (4 (d + f \[Nu]))) (E^(g + c Sqrt[z] + f z))^\[Nu] (2 E^((b + 2 d Sqrt[z] + c \[Nu] + 2 f Sqrt[z] \[Nu])^2/(4 (d + f \[Nu]))) Sqrt[d + f \[Nu]] - Sqrt[Pi] (b + c \[Nu]) Erfi[(b + 2 d Sqrt[z] + c \[Nu] + 2 f Sqrt[z] \[Nu])/ (2 Sqrt[d + f \[Nu]])]))

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List["\[Integral]", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["b", " ", SqrtBox["z"]]], " ", "+", RowBox[List["d", " ", "z"]]]]], " ", SuperscriptBox[RowBox[List["(", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List[SqrtBox["z"], " ", "c"]], "+", RowBox[List["f", " ", "z"]], "+", "g"]]], ")"]], "\[Nu]"], RowBox[List["\[DifferentialD]", "z"]]]]]], "\[Equal]", RowBox[List[FractionBox["1", RowBox[List["2", " ", SuperscriptBox[RowBox[List["(", RowBox[List["d", "+", RowBox[List["f", " ", "\[Nu]"]]]], ")"]], RowBox[List["3", "/", "2"]]]]]], RowBox[List["(", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["b", " ", SqrtBox["z"]]], "+", RowBox[List["d", " ", "z"]], "-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["b", "+", RowBox[List["2", " ", "d", " ", SqrtBox["z"]]], "+", RowBox[List[RowBox[List["(", RowBox[List["c", "+", RowBox[List["2", " ", "f", " ", SqrtBox["z"]]]]], ")"]], " ", "\[Nu]"]]]], ")"]], "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List["d", "+", RowBox[List["f", " ", "\[Nu]"]]]], ")"]]]]]]]], " ", SuperscriptBox[RowBox[List["(", SuperscriptBox["\[ExponentialE]", RowBox[List["g", "+", RowBox[List["c", " ", SqrtBox["z"]]], "+", RowBox[List["f", " ", "z"]]]]], ")"]], "\[Nu]"], " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", SuperscriptBox["\[ExponentialE]", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["b", "+", RowBox[List["2", " ", "d", " ", SqrtBox["z"]]], "+", RowBox[List["c", " ", "\[Nu]"]], "+", RowBox[List["2", " ", "f", " ", SqrtBox["z"], " ", "\[Nu]"]]]], ")"]], "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List["d", "+", RowBox[List["f", " ", "\[Nu]"]]]], ")"]]]]]], " ", SqrtBox[RowBox[List["d", "+", RowBox[List["f", " ", "\[Nu]"]]]]]]], "-", RowBox[List[SqrtBox["\[Pi]"], " ", RowBox[List["(", RowBox[List["b", "+", RowBox[List["c", " ", "\[Nu]"]]]], ")"]], " ", RowBox[List["Erfi", "[", FractionBox[RowBox[List["b", "+", RowBox[List["2", " ", "d", " ", SqrtBox["z"]]], "+", RowBox[List["c", " ", "\[Nu]"]], "+", RowBox[List["2", " ", "f", " ", SqrtBox["z"], " ", "\[Nu]"]]]], RowBox[List["2", " ", SqrtBox[RowBox[List["d", "+", RowBox[List["f", " ", "\[Nu]"]]]]]]]], "]"]]]]]], ")"]]]], ")"]]]]]]]]

 MathML Form

 z b + d z ( z c + f z + g ) ν z 1 2 ( d + f ν ) 3 / 2 ( - ( b + ( c + 2 f z ) ν + 2 d z ) 2 4 ( d + f ν ) + d z + b z ( z c + g + f z ) ν ( 2 ( b + c ν + 2 f z ν + 2 d z ) 2 4 ( d + f ν ) d + f ν - π ( b + c ν ) erfi ( b + c ν + 2 f z ν + 2 d z 2 d + f ν ) ) ) z z 1 2 b d z z 1 2 c f z g ν 1 2 d f ν 3 2 -1 -1 b c 2 f z 1 2 ν 2 d z 1 2 2 4 d f ν -1 d z b z 1 2 z 1 2 c g f z ν 2 b c ν 2 f z 1 2 ν 2 d z 1 2 2 4 d f ν -1 d f ν 1 2 -1 1 2 b c ν Erfi b c ν 2 f z 1 2 ν 2 d z 1 2 2 d f ν 1 2 -1 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["\[Integral]", RowBox[List[RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["b_", " ", SqrtBox["z_"]]], "+", RowBox[List["d_", " ", "z_"]]]]], " ", SuperscriptBox[RowBox[List["(", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List[SqrtBox["z_"], " ", "c_"]], "+", RowBox[List["f_", " ", "z_"]], "+", "g_"]]], ")"]], "\[Nu]_"]]], RowBox[List["\[DifferentialD]", "z_"]]]]]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["b", " ", SqrtBox["z"]]], "+", RowBox[List["d", " ", "z"]], "-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["b", "+", RowBox[List["2", " ", "d", " ", SqrtBox["z"]]], "+", RowBox[List[RowBox[List["(", RowBox[List["c", "+", RowBox[List["2", " ", "f", " ", SqrtBox["z"]]]]], ")"]], " ", "\[Nu]"]]]], ")"]], "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List["d", "+", RowBox[List["f", " ", "\[Nu]"]]]], ")"]]]]]]]], " ", SuperscriptBox[RowBox[List["(", SuperscriptBox["\[ExponentialE]", RowBox[List["g", "+", RowBox[List["c", " ", SqrtBox["z"]]], "+", RowBox[List["f", " ", "z"]]]]], ")"]], "\[Nu]"], " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", SuperscriptBox["\[ExponentialE]", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["b", "+", RowBox[List["2", " ", "d", " ", SqrtBox["z"]]], "+", RowBox[List["c", " ", "\[Nu]"]], "+", RowBox[List["2", " ", "f", " ", SqrtBox["z"], " ", "\[Nu]"]]]], ")"]], "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List["d", "+", RowBox[List["f", " ", "\[Nu]"]]]], ")"]]]]]], " ", SqrtBox[RowBox[List["d", "+", RowBox[List["f", " ", "\[Nu]"]]]]]]], "-", RowBox[List[SqrtBox["\[Pi]"], " ", RowBox[List["(", RowBox[List["b", "+", RowBox[List["c", " ", "\[Nu]"]]]], ")"]], " ", RowBox[List["Erfi", "[", FractionBox[RowBox[List["b", "+", RowBox[List["2", " ", "d", " ", SqrtBox["z"]]], "+", RowBox[List["c", " ", "\[Nu]"]], "+", RowBox[List["2", " ", "f", " ", SqrtBox["z"], " ", "\[Nu]"]]]], RowBox[List["2", " ", SqrtBox[RowBox[List["d", "+", RowBox[List["f", " ", "\[Nu]"]]]]]]]], "]"]]]]]], ")"]]]], RowBox[List["2", " ", SuperscriptBox[RowBox[List["(", RowBox[List["d", "+", RowBox[List["f", " ", "\[Nu]"]]]], ")"]], RowBox[List["3", "/", "2"]]]]]]]]]]

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

 2002-12-18