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/01.07.21.2595.01

 Input Form

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

 Standard Form

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 MathML Form

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

 Rule Form

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

 2002-12-18