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/01.07.21.2603.01

 Input Form

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

 Standard Form

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 MathML Form

 z b + e sin ( z a + q ) cos v ( z c + g ) z 2 - v ( z ( b - a ) + e - q ( ( b - a ) z - 1 ) ( b - a ) 2 - z ( b + a ) + e + q ( ( b + a ) z - 1 ) ( b + a ) 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 s = 0 v - 1 2 ( e - q + g ( v - 2 s ) + ( b - a + c ( v - 2 s ) ) z ( ( b - a + c ( v - 2 s ) ) z - 1 ) ( b - a + c ( v - 2 s ) ) 2 + e - q - g ( v - 2 s ) + ( b - a - c ( v - 2 s ) ) z ( ( b - a - c ( v - 2 s ) ) z - 1 ) ( b - a - c ( v - 2 s ) ) 2 - e + q + g ( v - 2 s ) + ( b + a + c ( v - 2 s ) ) z ( ( b + a + c ( v - 2 s ) ) z - 1 ) ( b + a + c ( v - 2 s ) ) 2 - e + q - g ( v - 2 s ) + ( b + a - c ( v - 2 s ) ) z ( ( b + a - c ( v - 2 s ) ) z - 1 ) ( b + a - c ( v - 2 s ) ) 2 ) ( v s ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["v", Identity]], List[TagBox["s", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] /; v + Condition z z 1 2 b e z 1 2 a q z 1 2 c g v 2 -1 v z 1 2 b -1 a e -1 q b -1 a z 1 2 -1 b -1 a 2 -1 -1 z 1 2 b a e q b a z 1 2 -1 b a 2 -1 Binomial v v 2 -1 1 -1 \$CellContext`v 2 2 -1 v s 0 v -1 2 -1 e -1 q g v -1 2 s b -1 a c v -1 2 s z 1 2 b -1 a c v -1 2 s z 1 2 -1 b -1 a c v -1 2 s 2 -1 e -1 q -1 g v -1 2 s b -1 a -1 c v -1 2 s z 1 2 b -1 a -1 c v -1 2 s z 1 2 -1 b -1 a -1 c v -1 2 s 2 -1 -1 e q g v -1 2 s b a c v -1 2 s z 1 2 b a c v -1 2 s z 1 2 -1 b a c v -1 2 s 2 -1 -1 e q -1 g v -1 2 s b a -1 c v -1 2 s z 1 2 b a -1 c v -1 2 s z 1 2 -1 b a -1 c v -1 2 s 2 -1 Binomial v s v SuperPlus [/itex]

 Rule Form

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

 2002-12-18