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/01.20.21.1276.01

 Input Form

 Integrate[E^(b Sqrt[z] + d z + e) Cos[a Sqrt[z] + p z + q] Cosh[c Sqrt[z] + f z + g], z] == (1/8) E^(e - g - I q) (2 (E^(((-I) a + b - c) Sqrt[z] + (d - f - I p) z)/(d - f - I p) + E^(2 g + ((-I) a + b + c) Sqrt[z] + (d + f - I p) z)/(d + f - I p) + E^(2 I q + (I a + b - c) Sqrt[z] + (d - f + I p) z)/(d - f + I p) + E^(2 g + 2 I q + (I a + b + c) Sqrt[z] + (d + f + I p) z)/ (d + f + I p)) - (((-I) a + b - c) E^((a + I (b - c))^2/(4 (d - f - I p))) Sqrt[Pi] Erfi[((-I) a + b - c + 2 (d - f - I p) Sqrt[z])/(2 Sqrt[d - f - I p])])/ (d - f - I p)^(3/2) - (((-I) a + b + c) E^(2 g + (a + I (b + c))^2/(4 (d + f - I p))) Sqrt[Pi] Erfi[((-I) a + b + c + 2 (d + f - I p) Sqrt[z])/(2 Sqrt[d + f - I p])])/ (d + f - I p)^(3/2) - ((I a + b - c) E^(-((I a + b - c)^2/(4 (d - f + I p))) + 2 I q) Sqrt[Pi] Erfi[(I a + b - c + 2 (d - f + I p) Sqrt[z])/(2 Sqrt[d - f + I p])])/ (d - f + I p)^(3/2) - ((I a + b + c) E^(2 g - (I a + b + c)^2/(4 (d + f + I p)) + 2 I q) Sqrt[Pi] Erfi[(I a + b + c + 2 (d + f + I p) Sqrt[z])/ (2 Sqrt[d + f + I p])])/(d + f + I p)^(3/2))

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List["\[Integral]", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["b", " ", SqrtBox["z"]]], "+", RowBox[List["d", " ", "z"]], "+", "e"]]], RowBox[List["Cos", "[", RowBox[List[RowBox[List["a", " ", SqrtBox["z"]]], "+", RowBox[List["p", " ", "z"]], "+", "q"]], "]"]], RowBox[List["Cosh", "[", RowBox[List[RowBox[List["c", " ", SqrtBox["z"]]], "+", RowBox[List["f", " ", "z"]], "+", "g"]], "]"]], RowBox[List["\[DifferentialD]", "z"]]]]]], "\[Equal]", RowBox[List[FractionBox["1", "8"], " ", SuperscriptBox["\[ExponentialE]", RowBox[List["e", "-", "g", "-", RowBox[List["\[ImaginaryI]", " ", "q"]]]]], " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", RowBox[List["(", RowBox[List[FractionBox[SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "a"]], "+", "b", "-", "c"]], ")"]], " ", SqrtBox["z"]]], "+", RowBox[List[RowBox[List["(", RowBox[List["d", 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RowBox[List[RowBox[List["2", " ", "g"]], "-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "a"]], "+", "b", "+", "c"]], ")"]], "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List["d", "+", "f", "+", RowBox[List["\[ImaginaryI]", " ", "p"]]]], ")"]]]]], "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", "q"]]]]], " ", SqrtBox["\[Pi]"], " ", RowBox[List["Erfi", "[", FractionBox[RowBox[List[RowBox[List["\[ImaginaryI]", " ", "a"]], "+", "b", "+", "c", "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["d", "+", "f", "+", RowBox[List["\[ImaginaryI]", " ", "p"]]]], ")"]], " ", SqrtBox["z"]]]]], RowBox[List["2", " ", SqrtBox[RowBox[List["d", "+", "f", "+", RowBox[List["\[ImaginaryI]", " ", "p"]]]]]]]], "]"]]]], SuperscriptBox[RowBox[List["(", RowBox[List["d", "+", "f", "+", RowBox[List["\[ImaginaryI]", " ", "p"]]]], ")"]], RowBox[List["3", "/", "2"]]]]]], ")"]]]]]]]]

 MathML Form

 z b + d z + e cos ( z a + p z + q ) cosh ( z c + f z + g ) z 1 8 e - g - q ( 2 ( z ( b + c + a ) + 2 g + 2 q + ( d + f + p ) z d + f + p + z ( b - c - a ) + ( d - f - p ) z d - f - p + z ( b + c - a ) + 2 g + ( d + f - p ) z d + f - p + z ( b - c + a ) + 2 q + ( d - f + p ) z d - f + p ) - ( b - c + a ) 2 q - ( b - c + a ) 2 4 ( d - f + p ) π erfi ( b - c + a + 2 ( d - f + p ) z 2 d - f + p ) ( d - f + p ) 3 / 2 - ( b + c + a ) - ( b + c + a ) 2 4 ( d + f + p ) + 2 g + 2 q π erfi ( b + c + a + 2 ( d + f + p ) z 2 d + f + p ) ( d + f + p ) 3 / 2 - ( b - c - a ) ( a + ( b - c ) ) 2 4 ( d - f - p ) π erfi ( b - c - a + 2 ( d - f - p ) z 2 d - f - p ) ( d - f - p ) 3 / 2 - ( b + c - a ) ( a + ( b + c ) ) 2 4 ( d + f - p ) + 2 g π erfi ( b + c - a + 2 ( d + f - p ) z 2 d + f - p ) ( d + f - p ) 3 / 2 ) z z 1 2 b d z e z 1 2 a p z q z 1 2 c f z g 1 8 e -1 g -1 q 2 z 1 2 b c a 2 g 2 q d f p z d f p -1 z 1 2 b -1 c -1 a d -1 f -1 p z d -1 f -1 p -1 z 1 2 b c -1 a 2 g d f -1 p z d f -1 p -1 z 1 2 b -1 c a 2 q d -1 f p z d -1 f p -1 -1 b -1 c a 2 q -1 b -1 c a 2 4 d -1 f p -1 1 2 Erfi b -1 c a 2 d -1 f p z 1 2 2 d -1 f p 1 2 -1 d -1 f p 3 2 -1 -1 b c a -1 b c a 2 4 d f p -1 2 g 2 q 1 2 Erfi b c a 2 d f p z 1 2 2 d f p 1 2 -1 d f p 3 2 -1 -1 b -1 c -1 a a b -1 c 2 4 d -1 f -1 p -1 1 2 Erfi b -1 c -1 a 2 d -1 f -1 p z 1 2 2 d -1 f -1 p 1 2 -1 d -1 f -1 p 3 2 -1 -1 b c -1 a a b c 2 4 d f -1 p -1 2 g 1 2 Erfi b c -1 a 2 d f -1 p z 1 2 2 d f -1 p 1 2 -1 d f -1 p 3 2 -1 [/itex]

 Rule Form

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

 2002-12-18