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/01.07.21.2587.01

 Input Form

 Integrate[E^(p Sqrt[z]) Sin[b Sqrt[z]] Cos[c z]^v, z] == 2^(-2 - v) (-((1/(b^2 + p^2)^2) (8 E^(p Sqrt[z]) Binomial[v, v/2] (-1 + Mod[v, 2]) ((-b) (-2 p + b^2 Sqrt[z] + p^2 Sqrt[z]) Cos[b Sqrt[z]] + (p^2 (-1 + p Sqrt[z]) + b^2 (1 + p Sqrt[z])) Sin[b Sqrt[z]]))) - I Sum[Binomial[v, s] (-(((b + I p) Sqrt[Pi] Erf[(b + I p + 2 c (-2 s + v) Sqrt[z])/ (2 Sqrt[I c (2 s - v)])])/(E^((I (b + I p)^2)/(c (8 s - 4 v))) (I c (2 s - v))^(3/2))) + ((I b + p) Sqrt[Pi] Erfi[((-I) b - p + 2 I c (-2 s + v) Sqrt[z])/ (2 Sqrt[I c (2 s - v)])])/(E^((I (b - I p)^2)/(c (8 s - 4 v))) (I c (2 s - v))^(3/2)) + (E^((I (b + I p)^2)/(c (8 s - 4 v))) (b + I p) Sqrt[Pi] Erfi[((-I) b + p + 2 I c (-2 s + v) Sqrt[z])/ (2 Sqrt[I c (-2 s + v)])])/(c (2 s - v) Sqrt[I c (-2 s + v)]) + (E^((I (b - I p)^2)/(c (8 s - 4 v))) (b - I p) Sqrt[Pi] Erfi[(I b + p + 2 I c (-2 s + v) Sqrt[z])/ (2 Sqrt[I c (-2 s + v)])])/(c (2 s - v) Sqrt[I c (-2 s + v)]) + (8 I E^(p Sqrt[z]) Sin[b Sqrt[z]] Sin[c (2 s - v) z])/(c (2 s - v))), {s, 0, Floor[(1/2) (-1 + v)]}]) /; Element[v, Integers] && v > 0

 Standard Form

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" ", SqrtBox["z"]]], "]"]], " ", RowBox[List["Sin", "[", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "s"]], "-", "v"]], ")"]], " ", "z"]], "]"]]]], RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "s"]], "-", "v"]], ")"]]]]]]], ")"]]]]]]]]]], ")"]]]]]], "/;", 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 - 2 ( - 1 ( b 2 + p 2 ) 2 ( 8 p z ( 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]]]]] ( v mod 2 \$CellContext`v 2 - 1 ) ( ( ( z p + 1 ) b 2 + p 2 ( p z - 1 ) ) sin ( b z ) - b ( z b 2 - 2 p + p 2 z ) cos ( b z ) ) ) - s = 0 v - 1 2 ( v s ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["v", Identity]], List[TagBox["s", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] ( - - ( b + p ) 2 c ( 8 s - 4 v ) ( b + p ) π erf ( b + p + 2 c ( v - 2 s ) z 2 c ( 2 s - v ) ) ( c ( 2 s - v ) ) 3 / 2 + - ( b - p ) 2 c ( 8 s - 4 v ) ( b + p ) π erfi ( - b - p + 2 c ( v - 2 s ) z 2 c ( 2 s - v ) ) ( c ( 2 s - v ) ) 3 / 2 + ( b + p ) 2 c ( 8 s - 4 v ) ( b + p ) π erfi ( - b + p + 2 c ( v - 2 s ) z 2 c ( v - 2 s ) ) c ( 2 s - v ) c ( v - 2 s ) + ( b - p ) 2 c ( 8 s - 4 v ) ( b - p ) π erfi ( b + p + 2 c ( v - 2 s ) z 2 c ( v - 2 s ) ) c ( 2 s - v ) c ( v - 2 s ) + 8 p z sin ( b z ) sin ( c ( 2 s - v ) z ) c ( 2 s - v ) ) ) /; v + Condition z p z 1 2 b z 1 2 c z v 2 -1 v -2 -1 1 b 2 p 2 2 -1 8 p z 1 2 Binomial v v 2 -1 \$CellContext`v 2 -1 z 1 2 p 1 b 2 p 2 p z 1 2 -1 b z 1 2 -1 b z 1 2 b 2 -1 2 p p 2 z 1 2 b z 1 2 -1 s 0 v -1 2 -1 Binomial v s -1 -1 b p 2 c 8 s -1 4 v -1 b p 1 2 Erf b p 2 c v -1 2 s z 1 2 2 c 2 s -1 v 1 2 -1 c 2 s -1 v 3 2 -1 -1 b -1 p 2 c 8 s -1 4 v -1 b p 1 2 Erfi -1 b -1 p 2 c v -1 2 s z 1 2 2 c 2 s -1 v 1 2 -1 c 2 s -1 v 3 2 -1 b p 2 c 8 s -1 4 v -1 b p 1 2 Erfi -1 b p 2 c v -1 2 s z 1 2 2 c v -1 2 s 1 2 -1 c 2 s -1 v c v -1 2 s 1 2 -1 b -1 p 2 c 8 s -1 4 v -1 b -1 p 1 2 Erfi b p 2 c v -1 2 s z 1 2 2 c v -1 2 s 1 2 -1 c 2 s -1 v c v -1 2 s 1 2 -1 8 p z 1 2 b z 1 2 c 2 s -1 v z c 2 s -1 v -1 v SuperPlus [/itex]

 Rule Form

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

 2002-12-18