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/01.20.21.3871.01

 Input Form

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

 Standard Form

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SuperscriptBox["b", "2"]]]]]]], ",", FractionBox[RowBox[List["\[ImaginaryI]", " ", "b", " ", SuperscriptBox["\[ExponentialE]", RowBox[List["\[ImaginaryI]", " ", "c", " ", "z"]]]]], RowBox[List["a", "-", SqrtBox[RowBox[List[SuperscriptBox["a", "2"], "-", SuperscriptBox["b", "2"]]]]]]]]], "]"]]]], ")"]]]], "-", RowBox[List[FractionBox["1", RowBox[List["d", "+", "e", "-", "p", "+", RowBox[List["\[ImaginaryI]", " ", "c", " ", "\[Beta]"]]]]], RowBox[List["(", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["-", RowBox[List["(", RowBox[List["d", "+", "e", "-", "p"]], ")"]]]], " ", "z"]]], " ", RowBox[List["AppellF1", "[", RowBox[List[FractionBox[RowBox[List["\[ImaginaryI]", " ", RowBox[List["(", RowBox[List["d", "+", "e", "-", "p", "+", RowBox[List["\[ImaginaryI]", " ", "c", " ", "\[Beta]"]]]], ")"]]]], "c"], ",", RowBox[List["-", "\[Beta]"]], ",", RowBox[List["-", "\[Beta]"]], ",", FractionBox[RowBox[List["c", "+", RowBox[List["\[ImaginaryI]", " ", RowBox[List["(", RowBox[List["d", "+", "e", "-", "p"]], ")"]]]], "-", RowBox[List["c", " ", "\[Beta]"]]]], "c"], ",", FractionBox[RowBox[List["\[ImaginaryI]", " ", "b", " ", SuperscriptBox["\[ExponentialE]", RowBox[List["\[ImaginaryI]", " ", "c", " ", "z"]]]]], RowBox[List["a", "+", SqrtBox[RowBox[List[SuperscriptBox["a", "2"], "-", SuperscriptBox["b", "2"]]]]]]], ",", FractionBox[RowBox[List["\[ImaginaryI]", " ", "b", " ", SuperscriptBox["\[ExponentialE]", RowBox[List["\[ImaginaryI]", " ", "c", " ", "z"]]]]], RowBox[List["a", "-", SqrtBox[RowBox[List[SuperscriptBox["a", "2"], "-", SuperscriptBox["b", "2"]]]]]]]]], "]"]]]], ")"]]]]]], ")"]], " "]]]]]]

 MathML Form

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

 Rule Form

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

 2002-12-18