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/01.07.21.2596.01

 Input Form

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

 Standard Form

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RowBox[List[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "b"]], "-", RowBox[List["\[ImaginaryI]", " ", "c", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]]]]]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "b"]], "+", RowBox[List["\[ImaginaryI]", " ", "c", " ", RowBox[List["(", 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 2 ) cos v ( c z 2 ) z 1 b ( 2 - v - 2 π ( v v 2 ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["v", Identity, Rule[Editable, True]]], List[TagBox[FractionBox["v", "2"], Identity, Rule[Editable, True]]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]], Rule[Editable, False]] ( - b - ( p 2 - 2 b π ) 4 b erfi ( p - 2 b z 2 - b ) - b ( p 2 - 2 b π ) 4 b erfi ( p + 2 b z 2 b ) ) ( 1 - v mod 2 \$CellContext`v 2 ) ) + 2 - v - 2 π s = 0 v - 1 2 ( v s ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["v", Identity, Rule[Editable, True]]], List[TagBox["s", Identity, Rule[Editable, True]]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]], Rule[Editable, False]] ( ( - p 2 - 2 π ( - b + c ( v - 2 s ) ) 4 ( - b + c ( v - 2 s ) ) - b + c ( v - 2 s ) ( b - c ( v - 2 s ) ) erfi ( p + 2 ( - b + c ( v - 2 s ) ) z 2 - b + c ( v - 2 s ) ) + - p 2 + 2 π ( b - c ( v - 2 s ) ) 4 ( b - c ( v - 2 s ) ) ( - b + c ( v - 2 s ) ) b - c ( v - 2 s ) erfi ( p - 2 ( - b + c ( v - 2 s ) ) z 2 b - c ( v - 2 s ) ) ) / ( ( b - c ( v - 2 s ) ) ( - b + c ( v - 2 s ) ) ) + ( - p 2 + 2 π ( b + c ( v - 2 s ) ) 4 ( b + c ( v - 2 s ) ) b + c ( v - 2 s ) ( - b - c ( v - 2 s ) ) erfi ( p + 2 ( b + c ( v - 2 s ) ) z 2 b + c ( v - 2 s ) ) + - p 2 - 2 π ( - b - c ( v - 2 s ) ) 4 ( - b - c ( v - 2 s ) ) ( b + c ( v - 2 s ) ) - b - c ( v - 2 s ) erfi ( p - 2 ( b + c ( v - 2 s ) ) z 2 - b - c ( v - 2 s ) ) ) / ( ( - b - c ( v - 2 s ) ) ( b + c ( v - 2 s ) ) ) ) /; v + Condition z p z b z 2 c z 2 v 1 b -1 2 -1 v -2 1 2 Binomial v v 2 -1 -1 b 1 2 -1 p 2 -1 2 b 4 b -1 Erfi p -1 2 b z 2 -1 b 1 2 -1 -1 b 1 2 p 2 -1 2 b 4 b -1 Erfi p 2 b z 2 b 1 2 -1 1 -1 \$CellContext`v 2 2 -1 v -2 1 2 s 0 v -1 2 -1 Binomial v s -1 p 2 -1 2 -1 b c v -1 2 s 4 -1 b c v -1 2 s -1 -1 b c v -1 2 s 1 2 b -1 c v -1 2 s Erfi p 2 -1 b c v -1 2 s z 2 -1 b c v -1 2 s 1 2 -1 -1 p 2 2 b -1 c v -1 2 s 4 b -1 c v -1 2 s -1 -1 b c v -1 2 s b -1 c v -1 2 s 1 2 Erfi p -1 2 -1 b c v -1 2 s z 2 b -1 c v -1 2 s 1 2 -1 b -1 c v -1 2 s -1 b c v -1 2 s -1 -1 p 2 2 b c v -1 2 s 4 b c v -1 2 s -1 b c v -1 2 s 1 2 -1 b -1 c v -1 2 s Erfi p 2 b c v -1 2 s z 2 b c v -1 2 s 1 2 -1 -1 p 2 -1 2 -1 b -1 c v -1 2 s 4 -1 b -1 c v -1 2 s -1 b c v -1 2 s -1 b -1 c v -1 2 s 1 2 Erfi p -1 2 b c v -1 2 s z 2 -1 b -1 c v -1 2 s 1 2 -1 -1 b -1 c v -1 2 s b c v -1 2 s -1 v SuperPlus [/itex]

 Rule Form

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

 2002-12-18