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/01.07.21.2445.01

 Input Form

 Integrate[z^n Sin[b z] Cos[c z^2]^v, z] == I 2^(-2 - v) (2 (I b)^(-1 - n) Binomial[v, v/2] ((-1)^n Gamma[1 + n, (-I) b z] + Gamma[1 + n, I b z]) (-1 + Mod[v, 2]) + I c^(-1 - 2 n) Sum[(-E^((I b^2)/(-8 c s + 4 c v))) (2 s - v)^(-1 - 2 n) Binomial[v, s] ((I c (-2 s + v))^n Sum[2^(-n + q) ((-I) b)^(n - q) (I (b + 4 c s z - 2 c v z))^(1 + q) (-((I (b + 4 c s z - 2 c v z)^2)/(c (2 s - v))))^((1/2) (-1 - q)) Binomial[n, q] Gamma[(1 + q)/2, -((I (b + 4 c s z - 2 c v z)^2)/ (c (8 s - 4 v)))], {q, 0, n}] + E^((I b^2)/(4 c s - 2 c v)) (I c (2 s - v))^n Sum[2^(-n + q) (I b)^(n - q) ((-I) (b + 4 c s z - 2 c v z))^(1 + q) ((I (b + 4 c s z - 2 c v z)^2)/(c (2 s - v)))^((1/2) (-1 - q)) Binomial[n, q] Gamma[(1 + q)/2, (I (b + 4 c s z - 2 c v z)^2)/ (8 c s - 4 c v)], {q, 0, n}] - E^((I b^2)/(4 c s - 2 c v)) (I c (2 s - v))^n Sum[2^(-n + q) ((-I) b)^(n - q) (I (b + 2 c (-2 s + v) z))^(1 + q) ((I (b + 2 c (-2 s + v) z)^2)/ (c (2 s - v)))^((1/2) (-1 - q)) Binomial[n, q] Gamma[(1 + q)/2, (I (b - 4 c s z + 2 c v z)^2)/(8 c s - 4 c v)], {q, 0, n}] - (I c (-2 s + v))^n Sum[2^(-n + q) (I b)^(n - q) ((-I) (b + 2 c (-2 s + v) z))^(1 + q) (-((I (b + 2 c (-2 s + v) z)^2)/(c (2 s - v))))^((1/2) (-1 - q)) Binomial[n, q] Gamma[(1 + q)/2, (b - 4 c s z + 2 c v z)^2/ (8 I c s - 4 I c v)], {q, 0, n}]), {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 ) cos v ( c z 2 ) z 2 - v - 2 ( 2 ( b ) - 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]]]]] ( ( - 1 ) n Γ ( n + 1 , - b z ) + Γ ( n + 1 , b z ) ) ( v mod 2 \$CellContext`v 2 - 1 ) + c - 1 - 2 n s = 0 v - 1 2 - b 2 4 c v - 8 c s ( 2 s - v ) - 2 n - 1 ( v s ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["v", Identity]], List[TagBox["s", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] ( - b 2 4 c s - 2 c v ( q = 0 n 2 q - n ( - b ) n - q ( ( b + 2 c ( v - 2 s ) z ) ) q + 1 ( ( b + 2 c ( v - 2 s ) z ) 2 c ( 2 s - v ) ) 1 2 ( - q - 1 ) ( n q ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["n", Identity]], List[TagBox["q", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] Γ ( q + 1 2 , ( b - 4 c s z + 2 c v z ) 2 8 c s - 4 c v ) ) ( c ( 2 s - v ) ) n + b 2 4 c s - 2 c v ( q = 0 n 2 q - n ( b ) n - q ( - ( b + 4 c s z - 2 c v z ) ) q + 1 ( ( b + 4 c s z - 2 c v z ) 2 c ( 2 s - v ) ) 1 2 ( - q - 1 ) ( n q ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["n", Identity]], List[TagBox["q", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] Γ ( q + 1 2 , ( b + 4 c s z - 2 c v z ) 2 8 c s - 4 c v ) ) ( c ( 2 s - v ) ) n + ( c ( v - 2 s ) ) n q = 0 n 2 q - n ( - b ) n - q ( ( b + 4 c s z - 2 c v z ) ) q + 1 ( - ( b + 4 c s z - 2 c v z ) 2 c ( 2 s - v ) ) 1 2 ( - q - 1 ) ( n q ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["n", Identity]], List[TagBox["q", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] Γ ( q + 1 2 , - ( b + 4 c s z - 2 c v z ) 2 c ( 8 s - 4 v ) ) - ( c ( v - 2 s ) ) n q = 0 n 2 q - n ( b ) n - q ( - ( b + 2 c ( v - 2 s ) z ) ) q + 1 ( - ( b + 2 c ( v - 2 s ) z ) 2 c ( 2 s - v ) ) 1 2 ( - q - 1 ) ( n q ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["n", Identity]], List[TagBox["q", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] Γ ( q + 1 2 , ( b - 4 c s z + 2 c v z ) 2 8 c s - 4 c v ) ) ) /; n v + Condition z z n b z c z 2 v 2 -1 v -2 2 b -1 n -1 Binomial v v 2 -1 -1 n Gamma n 1 -1 b z Gamma n 1 b z \$CellContext`v 2 -1 c -1 -1 2 n s 0 v -1 2 -1 -1 b 2 4 c v -1 8 c s -1 2 s -1 v -2 n -1 Binomial v s -1 b 2 4 c s -1 2 c v -1 q 0 n 2 q -1 n -1 b n -1 q b 2 c v -1 2 s z q 1 b 2 c v -1 2 s z 2 c 2 s -1 v -1 1 2 -1 q -1 Binomial n q Gamma q 1 2 -1 b -1 4 c s z 2 c v z 2 8 c s -1 4 c v -1 c 2 s -1 v n b 2 4 c s -1 2 c v -1 q 0 n 2 q -1 n b n -1 q -1 b 4 c s z -1 2 c v z q 1 b 4 c s z -1 2 c v z 2 c 2 s -1 v -1 1 2 -1 q -1 Binomial n q Gamma q 1 2 -1 b 4 c s z -1 2 c v z 2 8 c s -1 4 c v -1 c 2 s -1 v n c v -1 2 s n q 0 n 2 q -1 n -1 b n -1 q b 4 c s z -1 2 c v z q 1 -1 b 4 c s z -1 2 c v z 2 c 2 s -1 v -1 1 2 -1 q -1 Binomial n q Gamma q 1 2 -1 -1 b 4 c s z -1 2 c v z 2 c 8 s -1 4 v -1 -1 c v -1 2 s n q 0 n 2 q -1 n b n -1 q -1 b 2 c v -1 2 s z q 1 -1 b 2 c v -1 2 s z 2 c 2 s -1 v -1 1 2 -1 q -1 Binomial n q Gamma q 1 2 -1 b -1 4 c s z 2 c v z 2 8 c s -1 4 c v -1 n v SuperPlus [/itex]

 Rule Form

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

 2002-12-18