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/01.20.21.3898.01

 Input Form

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

 Standard Form

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

 MathML Form

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

 Rule Form

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

 2002-12-18