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/01.07.21.2460.01

 Input Form

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

 Standard Form

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 MathML Form

 z n sin ( b z 2 ) cos v ( c z 2 + g ) z - 2 - v - 2 ( v v 2 ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["v", Identity, Rule[Editable, True]]], List[TagBox[FractionBox["v", "2"], Identity, Rule[Editable, True]]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]], Rule[Editable, False]] ( ( b z 2 ) 1 2 ( - n - 1 ) Γ ( n + 1 2 , b z 2 ) - ( - b z 2 ) 1 2 ( - n - 1 ) Γ ( n + 1 2 , - b z 2 ) ) ( 1 - v mod 2 \$CellContext`v 2 ) z n + 1 - 2 - v - 2 z n + 1 s = 0 v - 1 2 ( v s ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["v", Identity, Rule[Editable, True]]], List[TagBox["s", Identity, Rule[Editable, True]]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]], Rule[Editable, False]] ( - - g ( v - 2 s ) Γ ( n + 1 2 , ( - b + c ( v - 2 s ) ) z 2 ) ( ( - b + c ( v - 2 s ) ) z 2 ) 1 2 ( - n - 1 ) + - g ( v - 2 s ) ( ( b + c ( v - 2 s ) ) z 2 ) 1 2 ( - n - 1 ) Γ ( n + 1 2 , ( b + c ( v - 2 s ) ) z 2 ) - g ( v - 2 s ) ( ( - b - c ( v - 2 s ) ) z 2 ) 1 2 ( - n - 1 ) Γ ( n + 1 2 , ( - b - c ( v - 2 s ) ) z 2 ) + g ( v - 2 s ) ( ( b - c ( v - 2 s ) ) z 2 ) 1 2 ( - n - 1 ) Γ ( n + 1 2 , ( b - c ( v - 2 s ) ) z 2 ) ) /; n v + Condition z z n b z 2 c z 2 g v -1 2 -1 v -2 Binomial v v 2 -1 b z 2 1 2 -1 n -1 Gamma n 1 2 -1 b z 2 -1 -1 b z 2 1 2 -1 n -1 Gamma n 1 2 -1 -1 b z 2 1 -1 \$CellContext`v 2 z n 1 -1 2 -1 v -2 z n 1 s 0 v -1 2 -1 Binomial v s -1 -1 g v -1 2 s Gamma n 1 2 -1 -1 b c v -1 2 s z 2 -1 b c v -1 2 s z 2 1 2 -1 n -1 -1 g v -1 2 s b c v -1 2 s z 2 1 2 -1 n -1 Gamma n 1 2 -1 b c v -1 2 s z 2 -1 g v -1 2 s -1 b -1 c v -1 2 s z 2 1 2 -1 n -1 Gamma n 1 2 -1 -1 b -1 c v -1 2 s z 2 g v -1 2 s b -1 c v -1 2 s z 2 1 2 -1 n -1 Gamma n 1 2 -1 b -1 c v -1 2 s z 2 n v SuperPlus [/itex]

 Rule Form

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

 2002-12-18