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/01.07.21.2593.01

 Input Form

 Integrate[E^(p z) Sin[b z] Cos[c Sqrt[z]]^v, z] == I 2^(-1 - v) (E^(((-I) b + p) z)/((-I) b + p) - E^((I b + p) z)/(I b + p)) Binomial[v, v/2] (1 - Mod[v, 2]) + 2^(-2 - v) I Sum[Binomial[v, s] ((4 E^(((-I) b + p) z) Cos[c (2 s - v) Sqrt[z]])/ ((-I) b + p) - (4 E^((I b + p) z) Cos[c (2 s - v) Sqrt[z]])/ (I b + p) + ((I c Sqrt[Pi])/((-I) b + p)^(3/2)) E^(I Pi - (-2 I c s + I c v)^2/(4 ((-I) b + p))) (-2 s + v) Erfi[(I c (-2 s + v) + 2 ((-I) b + p) Sqrt[z])/ (2 Sqrt[(-I) b + p])] + (((I c Sqrt[Pi])/(I b + p)^(3/2)) (2 s - v) Erfi[(I c (2 s - v) + 2 (I b + p) Sqrt[z])/(2 Sqrt[I b + p])])/ E^((2 I c s - I c v)^2/(4 (I b + p))) - (((I c Sqrt[Pi])/((-I) b + p)^(3/2)) (2 s - v) Erfi[(I c (2 s - v) + 2 ((-I) b + p) Sqrt[z])/(2 Sqrt[(-I) b + p])])/ E^((2 I c s - I c v)^2/(4 ((-I) b + p))) - ((I c Sqrt[Pi])/(I b + p)^(3/2)) E^((-I) Pi + (c^2 (-2 s + v)^2)/(4 (I b + p))) (-2 s + v) Erfi[(I c (-2 s + v) + 2 (I b + p) Sqrt[z])/(2 Sqrt[I b + p])]), {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 ( ( - b + p ) z - b + p - ( b + p ) z b + p ) ( 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 - 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]]]]] ( 4 ( - b + p ) z cos ( c ( 2 s - v ) z ) - b + p - 4 ( b + p ) z cos ( c ( 2 s - v ) z ) b + p - ( c π ) - ( 2 c s - c v ) 2 4 ( - b + p ) ( 2 s - v ) erfi ( 2 z ( - b + p ) + c ( 2 s - v ) 2 - b + p ) ( - b + p ) 3 / 2 + π - ( c v - 2 c s ) 2 4 ( - b + p ) ( c π ) ( v - 2 s ) erfi ( 2 z ( - b + p ) + c ( v - 2 s ) 2 - b + p ) ( - b + p ) 3 / 2 + - ( 2 c s - c v ) 2 4 ( b + p ) ( c π ) ( 2 s - v ) erfi ( 2 z ( b + p ) + c ( 2 s - v ) 2 b + p ) ( b + p ) 3 / 2 - ( c π ) c 2 ( v - 2 s ) 2 4 ( b + p ) - π ( v - 2 s ) erfi ( 2 z ( b + p ) + c ( v - 2 s ) 2 b + p ) ( b + p ) 3 / 2 ) /; v + Condition z p z b z c z 1 2 v 2 -1 v -1 -1 b p z -1 b p -1 -1 b p z b p -1 Binomial v v 2 -1 1 -1 \$CellContext`v 2 2 -1 v -2 s 0 v -1 2 -1 Binomial v s 4 -1 b p z c 2 s -1 v z 1 2 -1 b p -1 -1 4 b p z c 2 s -1 v z 1 2 b p -1 -1 c 1 2 -1 2 c s -1 c v 2 4 -1 b p -1 2 s -1 v Erfi 2 z 1 2 -1 b p c 2 s -1 v 2 -1 b p 1 2 -1 -1 b p 3 2 -1 -1 c v -1 2 c s 2 4 -1 b p -1 c 1 2 v -1 2 s Erfi 2 z 1 2 -1 b p c v -1 2 s 2 -1 b p 1 2 -1 -1 b p 3 2 -1 -1 2 c s -1 c v 2 4 b p -1 c 1 2 2 s -1 v Erfi 2 z 1 2 b p c 2 s -1 v 2 b p 1 2 -1 b p 3 2 -1 -1 c 1 2 c 2 v -1 2 s 2 4 b p -1 -1 v -1 2 s Erfi 2 z 1 2 b p c v -1 2 s 2 b p 1 2 -1 b p 3 2 -1 v SuperPlus [/itex]

 Rule Form

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

 2002-12-18