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 Cos

 http://functions.wolfram.com/01.07.21.2427.01

 Input Form

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

 Standard Form

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 MathML Form

 z α - 1 sin ( c z + d ) cos v ( a z + b ) z - 2 - v - 1 - d z α ( - ( 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]]]]] ( 2 d ( c z ) α Γ ( α , - c z ) - ( - c z ) α Γ ( α , c z ) ) ( 1 - v mod 2 \$CellContext`v 2 ) ( c 2 z 2 ) - α - s = 0 v - 1 2 - ( 2 b s + b v ) ( ( c + 2 a s - a v ) 2 z 2 ) - α ( ( c - 2 a s + a v ) 2 z 2 ) - α ( 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 b s ) ( ( c + 2 a s - a v ) z ) α Γ ( α , - ( c + 2 a s - a v ) z ) ( ( c - 2 a s + a v ) 2 z 2 ) α - 2 b v ( - ( c + 2 a s - a v ) z ) α Γ ( α , ( c + 2 a s - a v ) z ) ( ( c - 2 a s + a v ) 2 z 2 ) α + ( ( c + 2 a s - a v ) 2 z 2 ) α ( 2 ( d + b v ) ( ( c - 2 a s + a v ) z ) α Γ ( α , - ( c - 2 a s + a v ) z ) - 4 b s ( - ( c - 2 a s + a v ) z ) α Γ ( α , ( c - 2 a s + a v ) z ) ) ) ) /; v + Condition z z α -1 c z d a z b v -1 2 -1 v -1 -1 d z α -1 Binomial v v 2 -1 2 d c z α Gamma α -1 c z -1 -1 c z α Gamma α c z 1 -1 \$CellContext`v 2 c 2 z 2 -1 α -1 s 0 v -1 2 -1 -1 2 b s b v c 2 a s -1 a v 2 z 2 -1 α c -1 2 a s a v 2 z 2 -1 α Binomial v s 2 d 2 b s c 2 a s -1 a v z α Gamma α -1 c 2 a s -1 a v z c -1 2 a s a v 2 z 2 α -1 2 b v -1 c 2 a s -1 a v z α Gamma α c 2 a s -1 a v z c -1 2 a s a v 2 z 2 α c 2 a s -1 a v 2 z 2 α 2 d b v c -1 2 a s a v z α Gamma α -1 c -1 2 a s a v z -1 4 b s -1 c -1 2 a s a v z α Gamma α c -1 2 a s a v z v SuperPlus [/itex]

 Rule Form

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

 2002-12-18