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/01.20.21.0873.01

 Input Form

 Integrate[Cosh[d z] (a Sin[e z]^2 + b Cos[e z]^2)^\[Beta], z] == (1/2) (-((1/(-d + 2 I e \[Beta])) ((E^(d z) (((-a) (-1 + E^(2 I e z))^2 + b (1 + E^(2 I e z))^2)/ E^(2 I e z))^\[Beta] AppellF1[-((I d)/(2 e)) - \[Beta], -\[Beta], -\[Beta], 1 - (I d)/(2 e) - \[Beta], -(((-a + b) E^(2 I e z))/ (a + b + 2 Sqrt[a b])), ((-a + b) E^(2 I e z))/ (-a - b + 2 Sqrt[a b])])/(4^\[Beta] (1 - ((-a + b) E^(2 I e z))/(-a - b + 2 Sqrt[a b]))^\[Beta] (1 + ((-a + b) E^(2 I e z))/(a + b + 2 Sqrt[a b]))^\[Beta]))) - (1/(d + 2 I e \[Beta])) (((((-a) (-1 + E^(2 I e z))^2 + b (1 + E^(2 I e z))^2)/E^(2 I e z))^ \[Beta] AppellF1[(I d)/(2 e) - \[Beta], -\[Beta], -\[Beta], 1 + (I d)/(2 e) - \[Beta], -(((-a + b) E^(2 I e z))/ (a + b + 2 Sqrt[a b])), ((-a + b) E^(2 I e z))/ (-a - b + 2 Sqrt[a b])])/(4^\[Beta] E^(d z) (1 - ((-a + b) E^(2 I e z))/(-a - b + 2 Sqrt[a b]))^\[Beta] (1 + ((-a + b) E^(2 I e z))/(a + b + 2 Sqrt[a b]))^\[Beta])))

 Standard Form

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

 MathML Form

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

 Rule Form

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

 2002-12-18