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/01.07.21.2600.01

 Input Form

 Integrate[E^(p Sqrt[z]) Sin[b Sqrt[z]] Cos[c Sqrt[z]]^v, z] == (I ((E^(((-I) b + p) Sqrt[z]) (-1 + ((-I) b + p) Sqrt[z]))/((-I) b + p)^2 - (E^((I b + p) Sqrt[z]) (-1 + (I b + p) Sqrt[z]))/(I b + p)^2) Binomial[v, v/2] (1 - Mod[v, 2]))/2^v + (I Sum[((E^(((-I) b + p - I c (-2 s + v)) Sqrt[z]) (-1 + ((-I) b + p - I c (-2 s + v)) Sqrt[z]))/ ((-I) b + p - I c (-2 s + v))^2 - (E^((I b + p - I c (-2 s + v)) Sqrt[z]) (-1 + (I b + p - I c (-2 s + v)) Sqrt[z]))/ (I b + p - I c (-2 s + v))^2 + (E^(((-I) b + p + I c (-2 s + v)) Sqrt[z]) (-1 + ((-I) b + p + I c (-2 s + v)) Sqrt[z]))/ ((-I) b + p + I c (-2 s + v))^2 - (E^((I b + p + I c (-2 s + v)) Sqrt[z]) (-1 + (I b + p + I c (-2 s + v)) Sqrt[z]))/ (I b + p + I c (-2 s + v))^2) Binomial[v, s], {s, 0, Floor[(1/2) (-1 + v)]}])/2^v /; Element[v, Integers] && v > 0

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["\[Integral]", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["p", " ", SqrtBox["z"]]]], RowBox[List["Sin", "[", RowBox[List["b", " ", SqrtBox["z"]]], "]"]], SuperscriptBox[RowBox[List["Cos", "[", RowBox[List["c", " ", SqrtBox["z"]]], "]"]], "v"], RowBox[List["\[DifferentialD]", "z"]]]]]], "\[Equal]", RowBox[List[RowBox[List["\[ImaginaryI]", " ", SuperscriptBox["2", RowBox[List["-", "v"]]], " ", RowBox[List["(", RowBox[List[FractionBox[RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "b"]], "+", "p"]], ")"]], " ", SqrtBox["z"]]]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "b"]], "+", "p"]], ")"]], " ", SqrtBox["z"]]]]], ")"]]]], SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", 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")"]]]]]], ")"]], "2"]], "-", FractionBox[RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "b"]], "+", "p", "+", RowBox[List["\[ImaginaryI]", " ", "c", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]]]]]], ")"]], " ", SqrtBox["z"]]]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "b"]], "+", "p", "+", RowBox[List["\[ImaginaryI]", " ", "c", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]]]]]], ")"]], " ", SqrtBox["z"]]]]], ")"]]]], SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "b"]], "+", "p", "+", RowBox[List["\[ImaginaryI]", " ", "c", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]]]]]], ")"]], "2"]]]], ")"]], " ", RowBox[List["Binomial", "[", RowBox[List["v", ",", "s"]], "]"]]]]]]]]]]]], "/;", RowBox[List[RowBox[List["v", "\[Element]", "Integers"]], "\[And]", RowBox[List["v", ">", "0"]]]]]]]]

 MathML Form

 p z sin ( b z ) cos v ( c z ) z 2 - v ( ( - b + p ) z ( ( - b + p ) z - 1 ) ( - b + p ) 2 - ( b + p ) z ( ( b + p ) z - 1 ) ( b + p ) 2 ) ( v v 2 ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["v", Identity]], List[TagBox[FractionBox["v", "2"], Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] ( 1 - v mod 2 \$CellContext`v 2 ) + 2 - v s = 0 v - 1 2 ( ( - b + p + c ( v - 2 s ) ) z ( ( - b + p + c ( v - 2 s ) ) z - 1 ) ( - b + p + c ( v - 2 s ) ) 2 + ( - b + p - c ( v - 2 s ) ) z ( ( - b + p - c ( v - 2 s ) ) z - 1 ) ( - b + p - c ( v - 2 s ) ) 2 - ( b + p + c ( v - 2 s ) ) z ( ( b + p + c ( v - 2 s ) ) z - 1 ) ( b + p + c ( v - 2 s ) ) 2 - ( b + p - c ( v - 2 s ) ) z ( ( b + p - c ( v - 2 s ) ) z - 1 ) ( b + p - c ( v - 2 s ) ) 2 ) ( v s ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["v", Identity]], List[TagBox["s", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] /; v + Condition z p z 1 2 b z 1 2 c z 1 2 v 2 -1 v -1 b p z 1 2 -1 b p z 1 2 -1 -1 b p 2 -1 -1 b p z 1 2 b p z 1 2 -1 b p 2 -1 Binomial v v 2 -1 1 -1 \$CellContext`v 2 2 -1 v s 0 v -1 2 -1 -1 b p c v -1 2 s z 1 2 -1 b p c v -1 2 s z 1 2 -1 -1 b p c v -1 2 s 2 -1 -1 b p -1 c v -1 2 s z 1 2 -1 b p -1 c v -1 2 s z 1 2 -1 -1 b p -1 c v -1 2 s 2 -1 -1 b p c v -1 2 s z 1 2 b p c v -1 2 s z 1 2 -1 b p c v -1 2 s 2 -1 -1 b p -1 c v -1 2 s z 1 2 b p -1 c v -1 2 s z 1 2 -1 b p -1 c v -1 2 s 2 -1 Binomial v s v SuperPlus [/itex]

 Rule Form

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

 2002-12-18