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/01.07.21.2461.01

 Input Form

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

 Standard Form

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 MathML Form

 z n sin ( z b ) cos v ( z c + g ) z ( - 1 ) n 2 - v b - 2 ( n + 1 ) ( 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]]]]] ( Γ ( 2 ( n + 1 ) , b z ) - Γ ( 2 ( n + 1 ) , - b z ) ) ( 1 - v mod 2 \$CellContext`v 2 ) - 2 - v z n + 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]]]]] ( - - g ( v - 2 s ) Γ ( 2 ( n + 1 ) , ( - b + c ( v - 2 s ) ) z ) ( ( - b + c ( v - 2 s ) ) z ) - 2 ( n + 1 ) + - g ( v - 2 s ) ( ( b + c ( v - 2 s ) ) z ) - 2 ( n + 1 ) Γ ( 2 ( n + 1 ) , ( b + c ( v - 2 s ) ) z ) - g ( v - 2 s ) ( ( - b - c ( v - 2 s ) ) z ) - 2 ( n + 1 ) Γ ( 2 ( n + 1 ) , ( - b - c ( v - 2 s ) ) z ) + g ( v - 2 s ) ( ( b - c ( v - 2 s ) ) z ) - 2 ( n + 1 ) Γ ( 2 ( n + 1 ) , ( b - c ( v - 2 s ) ) z ) ) /; n v + Condition z z n z 1 2 b z 1 2 c g v -1 n 2 -1 v b -2 n 1 Binomial v v 2 -1 Gamma 2 n 1 b z 1 2 -1 Gamma 2 n 1 -1 b z 1 2 1 -1 \$CellContext`v 2 -1 2 -1 v z n 1 s 0 v -1 2 -1 Binomial v s -1 -1 g v -1 2 s Gamma 2 n 1 -1 b c v -1 2 s z 1 2 -1 b c v -1 2 s z 1 2 -2 n 1 -1 g v -1 2 s b c v -1 2 s z 1 2 -2 n 1 Gamma 2 n 1 b c v -1 2 s z 1 2 -1 g v -1 2 s -1 b -1 c v -1 2 s z 1 2 -2 n 1 Gamma 2 n 1 -1 b -1 c v -1 2 s z 1 2 g v -1 2 s b -1 c v -1 2 s z 1 2 -2 n 1 Gamma 2 n 1 b -1 c v -1 2 s z 1 2 n v SuperPlus [/itex]

 Rule Form

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

 2002-12-18