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/01.07.21.2589.01

 Input Form

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

 Standard Form

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"2"]]]]]], ")"]]]]]]]]]]]], "/;", 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 ( 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]]]]] ( 4 p z cos ( b z ) b - - p 2 4 b p π erfi ( p - 2 b z 2 - b ) ( - b ) 3 / 2 - p 2 4 b - π p π erfi ( p + 2 b z 2 b ) ( b ) 3 / 2 ) ( 1 - v mod 2 \$CellContext`v 2 ) - 2 - v - 2 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]]]]] ( 2 p z ( 2 cosh ( ( - b + 2 c s - c v ) z ) b + c ( v - 2 s ) + 2 cosh ( ( b + 2 c s - c v ) z ) b + 2 c s - c v ) + - p 2 4 ( b + c ( v - 2 s ) ) - π p π erfi ( p + 2 ( b + c ( v - 2 s ) ) z 2 b + c ( v - 2 s ) ) ( b + c ( v - 2 s ) ) 3 / 2 + - p 2 4 ( - b - c ( v - 2 s ) ) p π erfi ( p + 2 ( - b - c ( v - 2 s ) ) z 2 - b - c ( v - 2 s ) ) ( - b - c ( v - 2 s ) ) 3 / 2 - π - p 2 4 ( - b + c ( v - 2 s ) ) p π erfi ( p + 2 ( - b + c ( v - 2 s ) ) z 2 - b + c ( v - 2 s ) ) ( - b + c ( v - 2 s ) ) 3 / 2 - - p 2 4 ( b - c ( v - 2 s ) ) p π erfi ( p + 2 ( b - c ( v - 2 s ) ) z 2 b - c ( v - 2 s ) ) ( b - c ( v - 2 s ) ) 3 / 2 ) /; v + Condition z p z 1 2 b z c z v 2 -1 v -2 Binomial v v 2 -1 4 p z 1 2 b z b -1 -1 -1 p 2 4 b -1 p 1 2 Erfi p -1 2 b z 1 2 2 -1 b 1 2 -1 -1 b 3 2 -1 -1 p 2 4 b -1 -1 p 1 2 Erfi p 2 b z 1 2 2 b 1 2 -1 b 3 2 -1 1 -1 \$CellContext`v 2 -1 2 -1 v -2 s 0 v -1 2 -1 Binomial v s 2 p z 1 2 2 -1 b 2 c s -1 c v z b c v -1 2 s -1 2 b 2 c s -1 c v z b 2 c s -1 c v -1 -1 p 2 4 b c v -1 2 s -1 -1 p 1 2 Erfi p 2 b c v -1 2 s z 1 2 2 b c v -1 2 s 1 2 -1 b c v -1 2 s 3 2 -1 -1 p 2 4 -1 b -1 c v -1 2 s -1 p 1 2 Erfi p 2 -1 b -1 c v -1 2 s z 1 2 2 -1 b -1 c v -1 2 s 1 2 -1 -1 b -1 c v -1 2 s 3 2 -1 -1 -1 p 2 4 -1 b c v -1 2 s -1 p 1 2 Erfi p 2 -1 b c v -1 2 s z 1 2 2 -1 b c v -1 2 s 1 2 -1 -1 b c v -1 2 s 3 2 -1 -1 -1 p 2 4 b -1 c v -1 2 s -1 p 1 2 Erfi p 2 b -1 c v -1 2 s z 1 2 2 b -1 c v -1 2 s 1 2 -1 b -1 c v -1 2 s 3 2 -1 v SuperPlus [/itex]

 Rule Form

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

 2002-12-18