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 Cos

 http://functions.wolfram.com/01.07.21.2733.01

 Input Form

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

 Standard Form

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 MathML Form

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

 Rule Form

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

 2002-12-18