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; }

 Cosh

 http://functions.wolfram.com/01.20.21.4741.01

 Input Form

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

 Standard Form

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

 MathML Form

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

 Rule Form

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

 2002-12-18