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/01.03.21.0517.01

 Input Form

 Integrate[(a E^(2 d z) + b E^(d z) + c)^\[Beta], z] == (1/(2 d \[Beta])) (((c + b E^(d z) + a E^(2 d z))^\[Beta] AppellF1[-2 \[Beta], -\[Beta], -\[Beta], 1 - 2 \[Beta], -((b + Sqrt[b^2 - 4 a c])/(E^(d z) (2 a))), (-b + Sqrt[b^2 - 4 a c])/ (E^(d z) (2 a))])/((1 - (-b + Sqrt[b^2 - 4 a c])/(E^(d z) (2 a)))^ \[Beta] (1 + (b + Sqrt[b^2 - 4 a c])/(E^(d z) (2 a)))^\[Beta]))

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List["\[Integral]", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["a", " ", SuperscriptBox["\[ExponentialE]", RowBox[List["2", "d", " ", "z"]]]]], "+", RowBox[List["b", " ", SuperscriptBox["\[ExponentialE]", RowBox[List["d", " ", "z"]]]]], "+", "c"]], ")"]], "\[Beta]"], RowBox[List["\[DifferentialD]", "z"]]]]]], "\[Equal]", RowBox[List[FractionBox["1", RowBox[List["2", " ", "d", " ", "\[Beta]"]]], RowBox[List["(", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", FractionBox[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "b"]], "+", SqrtBox[RowBox[List[SuperscriptBox["b", "2"], "-", RowBox[List["4", " ", "a", " ", "c"]]]]]]], ")"]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["-", "d"]], " ", "z"]]]]], RowBox[List["2", " ", "a"]]]]], ")"]], RowBox[List["-", "\[Beta]"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", FractionBox[RowBox[List[RowBox[List["(", RowBox[List["b", "+", SqrtBox[RowBox[List[SuperscriptBox["b", "2"], "-", RowBox[List["4", " ", "a", " ", "c"]]]]]]], ")"]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["-", "d"]], " ", "z"]]]]], RowBox[List["2", " ", "a"]]]]], ")"]], RowBox[List["-", "\[Beta]"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["c", "+", RowBox[List["b", " ", SuperscriptBox["\[ExponentialE]", RowBox[List["d", " ", "z"]]]]], "+", RowBox[List["a", " ", SuperscriptBox["\[ExponentialE]", RowBox[List["2", " ", "d", " ", "z"]]]]]]], ")"]], "\[Beta]"], " ", RowBox[List["AppellF1", "[", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "\[Beta]"]], ",", RowBox[List["-", "\[Beta]"]], ",", RowBox[List["-", "\[Beta]"]], ",", RowBox[List["1", "-", RowBox[List["2", " ", "\[Beta]"]]]], ",", RowBox[List["-", FractionBox[RowBox[List[RowBox[List["(", RowBox[List["b", "+", SqrtBox[RowBox[List[SuperscriptBox["b", "2"], "-", RowBox[List["4", " ", "a", " ", "c"]]]]]]], ")"]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["-", "d"]], " ", "z"]]]]], RowBox[List["2", " ", "a"]]]]], ",", FractionBox[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "b"]], "+", SqrtBox[RowBox[List[SuperscriptBox["b", "2"], "-", RowBox[List["4", " ", "a", " ", "c"]]]]]]], ")"]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["-", "d"]], " ", "z"]]]]], RowBox[List["2", " ", "a"]]]]], "]"]]]], ")"]]]]]]]]

 MathML Form

 ( 2 d z a + b d z + c ) β z 1 2 d β ( ( 1 - ( b 2 - 4 a c - b ) - d z 2 a ) - β ( - d z ( b + b 2 - 4 a c ) 2 a + 1 ) - β ( 2 d z a + b d z + c ) β F 1 AppellF1 ( - 2 β ; - β , - β ; 1 - 2 β ; - ( b + b 2 - 4 a c ) - d z 2 a , ( b 2 - 4 a c - b ) - d z 2 a ) ) z 2 d z a b d z c β 1 2 d β -1 1 -1 b 2 -1 4 a c 1 2 -1 b -1 d z 2 a -1 -1 β -1 d z b b 2 -1 4 a c 1 2 2 a -1 1 -1 β 2 d z a b d z c β AppellF1 -2 β -1 β -1 β 1 -1 2 β -1 b b 2 -1 4 a c 1 2 -1 d z 2 a -1 b 2 -1 4 a c 1 2 -1 b -1 d z 2 a -1 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["\[Integral]", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["a_", " ", SuperscriptBox["\[ExponentialE]", RowBox[List["2", " ", "d_", " ", "z_"]]]]], "+", RowBox[List["b_", " ", SuperscriptBox["\[ExponentialE]", RowBox[List["d_", " ", "z_"]]]]], "+", "c_"]], ")"]], "\[Beta]_"], RowBox[List["\[DifferentialD]", "z_"]]]]]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", FractionBox[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "b"]], "+", SqrtBox[RowBox[List[SuperscriptBox["b", "2"], "-", RowBox[List["4", " ", "a", " ", "c"]]]]]]], ")"]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["-", "d"]], " ", "z"]]]]], RowBox[List["2", " ", "a"]]]]], ")"]], RowBox[List["-", "\[Beta]"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", FractionBox[RowBox[List[RowBox[List["(", RowBox[List["b", "+", SqrtBox[RowBox[List[SuperscriptBox["b", "2"], "-", RowBox[List["4", " ", "a", " ", "c"]]]]]]], ")"]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["-", "d"]], " ", "z"]]]]], RowBox[List["2", " ", "a"]]]]], ")"]], RowBox[List["-", "\[Beta]"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["c", "+", RowBox[List["b", " ", SuperscriptBox["\[ExponentialE]", RowBox[List["d", " ", "z"]]]]], "+", RowBox[List["a", " ", SuperscriptBox["\[ExponentialE]", RowBox[List["2", " ", "d", " ", "z"]]]]]]], ")"]], "\[Beta]"], " ", RowBox[List["AppellF1", "[", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "\[Beta]"]], ",", RowBox[List["-", "\[Beta]"]], ",", RowBox[List["-", "\[Beta]"]], ",", RowBox[List["1", "-", RowBox[List["2", " ", "\[Beta]"]]]], ",", RowBox[List["-", FractionBox[RowBox[List[RowBox[List["(", RowBox[List["b", "+", SqrtBox[RowBox[List[SuperscriptBox["b", "2"], "-", RowBox[List["4", " ", "a", " ", "c"]]]]]]], ")"]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["-", "d"]], " ", "z"]]]]], RowBox[List["2", " ", "a"]]]]], ",", FractionBox[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "b"]], "+", SqrtBox[RowBox[List[SuperscriptBox["b", "2"], "-", RowBox[List["4", " ", "a", " ", "c"]]]]]]], ")"]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["-", "d"]], " ", "z"]]]]], RowBox[List["2", " ", "a"]]]]], "]"]]]], RowBox[List["2", " ", "d", " ", "\[Beta]"]]]]]]]

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

 2002-12-18