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/01.07.21.2447.01

 Input Form

 Integrate[z^n Sin[d z + e] Cos[c z^2]^v, z] == 2^(-2 - v) ((2 d^(-1 - 2 n) Binomial[v, v/2] ((I d)^n E^(2 I e) Gamma[1 + n, (-I) d z] + ((-I) d)^n Gamma[1 + n, I d z]) (-1 + Mod[v, 2]))/E^(I e) - (1/c) (((-1)^n Sum[((2 s - v)^(-1 - 2 n) Binomial[v, s] ((-E^(2 I e)) (I c (-2 s + v))^n Sum[2^(-n + q) ((-I) d)^(n - q) (I (d + 4 c s z - 2 c v z))^(1 + q) (-((I (d + 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 (d + 4 c s z - 2 c v z)^2)/(c (8 s - 4 v)))], {q, 0, n}] - E^((I d^2)/(4 c s - 2 c v)) (I c (2 s - v))^n Sum[2^(-n + q) (I d)^(n - q) ((-I) (d + 4 c s z - 2 c v z))^(1 + q) ((I (d + 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 (d + 4 c s z - 2 c v z)^2)/(8 c s - 4 c v)], {q, 0, n}] + E^(2 I (e + d^2/(8 c s - 4 c v))) (I c (2 s - v))^n Sum[2^(-n + q) ((-I) d)^(n - q) (I (d + 2 c (-2 s + v) z))^(1 + q) ((I (d + 2 c (-2 s + v) z)^2)/(c (2 s - v)))^((1/2) (-1 - q)) Binomial[n, q] Gamma[(1 + q)/2, (I (d - 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 d)^(n - q) ((-I) (d + 2 c (-2 s + v) z))^(1 + q) (-((I (d + 2 c (-2 s + v) z)^2)/(c (2 s - v))))^((1/2) (-1 - q)) Binomial[n, q] Gamma[(1 + q)/2, (d - 4 c s z + 2 c v z)^2/(8 I c s - 4 I c v)], {q, 0, n}]))/ E^(I (e + d^2/(8 c s - 4 c v))), {s, 0, Floor[(1/2) (-1 + v)]}])/ (I c)^(2 n))) /; Element[n, Integers] && n >= 0 && Element[v, Integers] && v > 0

 Standard Form

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 MathML Form

 z n sin ( e + d z ) cos v ( c z 2 ) z 2 - v - 2 ( 2 d - 2 n - 1 - e ( 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 ( n + 1 , d z ) ( - d ) n + ( d ) n 2 e Γ ( n + 1 , - d z ) ) ( v mod 2 \$CellContext`v 2 - 1 ) - 1 c ( ( - 1 ) n ( c ) - 2 n s = 0 v - 1 2 - ( d 2 8 c s - 4 c v + e ) ( 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]]]]] ( 2 ( d 2 8 c s - 4 c v + e ) ( q = 0 n 2 q - n ( - d ) n - q ( ( d + 2 c ( v - 2 s ) z ) ) q + 1 ( ( d + 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 , ( d - 4 c s z + 2 c v z ) 2 8 c s - 4 c v ) ) ( c ( 2 s - v ) ) n - d 2 4 c s - 2 c v ( q = 0 n 2 q - n ( d ) n - q ( - ( d + 4 c s z - 2 c v z ) ) q + 1 ( ( d + 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 , ( d + 4 c s z - 2 c v z ) 2 8 c s - 4 c v ) ) ( c ( 2 s - v ) ) n - 2 e ( c ( v - 2 s ) ) n q = 0 n 2 q - n ( - d ) n - q ( ( d + 4 c s z - 2 c v z ) ) q + 1 ( - ( d + 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 , - ( d + 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 ( d ) n - q ( - ( d + 2 c ( v - 2 s ) z ) ) q + 1 ( - ( d + 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 , ( d - 4 c s z + 2 c v z ) 2 8 c s - 4 c v ) ) ) ) /; n v + Condition z z n e d z c z 2 v 2 -1 v -2 2 d -2 n -1 -1 e Binomial v v 2 -1 Gamma n 1 d z -1 d n d n 2 e Gamma n 1 -1 d z \$CellContext`v 2 -1 -1 1 c -1 -1 n c -2 n s 0 v -1 2 -1 -1 d 2 8 c s -1 4 c v -1 e 2 s -1 v -2 n -1 Binomial v s 2 d 2 8 c s -1 4 c v -1 e q 0 n 2 q -1 n -1 d n -1 q d 2 c v -1 2 s z q 1 d 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 d -1 4 c s z 2 c v z 2 8 c s -1 4 c v -1 c 2 s -1 v n -1 d 2 4 c s -1 2 c v -1 q 0 n 2 q -1 n d n -1 q -1 d 4 c s z -1 2 c v z q 1 d 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 d 4 c s z -1 2 c v z 2 8 c s -1 4 c v -1 c 2 s -1 v n -1 2 e c v -1 2 s n q 0 n 2 q -1 n -1 d n -1 q d 4 c s z -1 2 c v z q 1 -1 d 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 d 4 c s z -1 2 c v z 2 c 8 s -1 4 v -1 c v -1 2 s n q 0 n 2 q -1 n d n -1 q -1 d 2 c v -1 2 s z q 1 -1 d 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 d -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