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 Cos

 http://functions.wolfram.com/01.07.21.2731.01

 Input Form

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

 Standard Form

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 MathML Form

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

 Rule Form

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

 2002-12-18