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; }

 Cos

 http://functions.wolfram.com/01.07.21.2418.01

 Input Form

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

 Standard Form

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 MathML Form

 ( a sin 2 ( e z ) + b sin ( 2 e z ) + c cos 2 ( e z ) ) β z 1 e β ( 2 - 2 β - 1 ( 2 e z ( - a - 2 b + c ) a + c - 2 a c - b 2 + 1 ) - β ( 2 e z ( - a - 2 b + c ) a + c + 2 a c - b 2 + 1 ) - β ( - 2 e z ( ( 1 + 2 e z ) ( c ( 1 + 2 e z ) - 2 b ( - 1 + 2 e z ) ) - a ( - 1 + 2 e z ) 2 ) ) β F 1 AppellF1 ( - β ; - β , - β ; 1 - β ; ( a - c + 2 b ) 2 e z a + c + 2 a c - b 2 , - ( - a - 2 b + c ) 2 e z a + c - 2 a c - b 2 ) ) z a e z 2 b 2 e z c e z 2 β 1 e β -1 2 -2 β -1 2 e z -1 a -1 2 b c a c -1 2 a c -1 b 2 1 2 -1 1 -1 β 2 e z -1 a -1 2 b c a c 2 a c -1 b 2 1 2 -1 1 -1 β -2 e z 1 2 e z c 1 2 e z -1 2 b -1 2 e z -1 a -1 2 e z 2 β AppellF1 -1 β -1 β -1 β 1 -1 β a -1 c 2 b 2 e z a c 2 a c -1 b 2 1 2 -1 -1 -1 a -1 2 b c 2 e z a c -1 2 a c -1 b 2 1 2 -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[RowBox[List["Sin", "[", RowBox[List["e_", " ", "z_"]], "]"]], "2"]]], "+", RowBox[List["b_", " ", RowBox[List["Sin", "[", RowBox[List["2", " ", "e_", " ", "z_"]], "]"]]]], "+", RowBox[List["c_", " ", SuperscriptBox[RowBox[List["Cos", "[", RowBox[List["e_", " ", "z_"]], "]"]], "2"]]]]], ")"]], "\[Beta]_"], RowBox[List["\[DifferentialD]", "z_"]]]]]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List["\[ImaginaryI]", " ", SuperscriptBox["2", RowBox[List[RowBox[List["-", "1"]], "-", RowBox[List["2", " ", "\[Beta]"]]]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", FractionBox[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "a"]], "-", RowBox[List["2", " ", "\[ImaginaryI]", " ", "b"]], "+", "c"]], ")"]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List["2", " ", "\[ImaginaryI]", " ", "e", " ", "z"]]]]], RowBox[List["a", "+", "c", "-", RowBox[List["2", " ", SqrtBox[RowBox[List[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[RowBox[List["-", "a"]], "-", RowBox[List["2", " ", "\[ImaginaryI]", " ", "b"]], "+", "c"]], ")"]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List["2", " ", "\[ImaginaryI]", " ", "e", " ", "z"]]]]], RowBox[List["a", "+", "c", "+", RowBox[List["2", " ", SqrtBox[RowBox[List[RowBox[List["-", SuperscriptBox["b", "2"]]], "+", RowBox[List["a", " ", "c"]]]]]]]]]]]], ")"]], RowBox[List["-", "\[Beta]"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["-", "2"]], " ", "\[ImaginaryI]", " ", "e", " ", "z"]]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "a"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", SuperscriptBox["\[ExponentialE]", RowBox[List["2", " ", "\[ImaginaryI]", " ", "e", " ", "z"]]]]], ")"]], "2"]]], "+", RowBox[List[RowBox[List["(", RowBox[List["1", "+", SuperscriptBox["\[ExponentialE]", RowBox[List["2", " ", "\[ImaginaryI]", " ", "e", " ", "z"]]]]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "\[ImaginaryI]", " ", "b", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", SuperscriptBox["\[ExponentialE]", RowBox[List["2", " ", "\[ImaginaryI]", " ", "e", " ", "z"]]]]], ")"]]]], "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List["1", "+", SuperscriptBox["\[ExponentialE]", RowBox[List["2", " ", "\[ImaginaryI]", " ", "e", " ", "z"]]]]], ")"]]]]]], ")"]]]]]], ")"]]]], ")"]], "\[Beta]"], " ", RowBox[List["AppellF1", "[", RowBox[List[RowBox[List["-", "\[Beta]"]], ",", RowBox[List["-", "\[Beta]"]], ",", RowBox[List["-", "\[Beta]"]], ",", RowBox[List["1", "-", "\[Beta]"]], ",", FractionBox[RowBox[List[RowBox[List["(", RowBox[List["a", "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", "b"]], "-", "c"]], ")"]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List["2", " ", "\[ImaginaryI]", " ", "e", " ", "z"]]]]], RowBox[List["a", "+", "c", "+", RowBox[List["2", " ", SqrtBox[RowBox[List[RowBox[List["-", SuperscriptBox["b", "2"]]], "+", RowBox[List["a", " ", "c"]]]]]]]]]], ",", RowBox[List["-", FractionBox[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "a"]], "-", RowBox[List["2", " ", "\[ImaginaryI]", " ", "b"]], "+", "c"]], ")"]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List["2", " ", "\[ImaginaryI]", " ", "e", " ", "z"]]]]], RowBox[List["a", "+", "c", "-", RowBox[List["2", " ", SqrtBox[RowBox[List[RowBox[List["-", SuperscriptBox["b", "2"]]], "+", RowBox[List["a", " ", "c"]]]]]]]]]]]]]], "]"]]]], RowBox[List["e", " ", "\[Beta]"]]]]]]]

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

 2002-12-18