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 Cosh

 http://functions.wolfram.com/01.20.21.3908.01

 Input Form

 Integrate[z^(\[Alpha] - 1) E^(p z) Sin[c z] Cosh[b + a z]^v, z] == 2^(-1 - v) z^\[Alpha] I (Binomial[v, v/2] (Gamma[\[Alpha], (-I) c z - p z]/ (((-I) c - p) z)^\[Alpha] - Gamma[\[Alpha], I c z - p z]/ (I (c + I p) z)^\[Alpha]) (1 - Mod[v, 2]) - Sum[(Binomial[v, s] (((-E^(2 b v)) Gamma[\[Alpha], ((-I) c - p + 2 a s - a v) z])/(((-I) c - p + 2 a s - a v) z)^ \[Alpha] + (E^(2 b v) Gamma[\[Alpha], (I c - p + 2 a s - a v) z])/ ((I c - p + 2 a s - a v) z)^\[Alpha] + E^(4 b s) ((-(((-I) c - p - 2 a s + a v) z)^(-\[Alpha])) Gamma[\[Alpha], ((-I) c - p - 2 a s + a v) z] + Gamma[\[Alpha], (I c - p - 2 a s + a v) z]/ ((I c - p - 2 a s + a v) z)^\[Alpha])))/E^(b (2 s + v)), {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 sin ( c z ) cosh v ( b + a z ) z 2 - v - 1 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]]]]] ( ( ( - c - p ) z ) - α Γ ( α , - c z - p z ) - ( ( c + p ) z ) - α Γ ( α , c z - p z ) ) ( 1 - v mod 2 \$CellContext`v 2 ) - s = 0 v - 1 2 - b ( 2 s + v ) ( v s ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["v", Identity]], List[TagBox["s", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] ( - 2 b v Γ ( α , ( - c - p + 2 a s - a v ) z ) ( ( - c - p + 2 a s - a v ) z ) - α + 4 b s ( ( ( c - p - 2 a s + a v ) z ) - α Γ ( α , ( c - p - 2 a s + a v ) z ) - ( ( - c - p - 2 a s + a v ) z ) - α Γ ( α , ( - c - p - 2 a s + a v ) z ) ) + 2 b v ( ( c - p + 2 a s - a v ) z ) - α Γ ( α , ( c - p + 2 a s - a v ) z ) ) ) /; v + Condition z z α -1 p z c z b a z v 2 -1 v -1 z α Binomial v v 2 -1 -1 c -1 p z -1 α Gamma α -1 c z -1 p z -1 c p z -1 α Gamma α c z -1 p z 1 -1 \$CellContext`v 2 -1 s 0 v -1 2 -1 -1 b 2 s v Binomial v s -1 2 b v Gamma α -1 c -1 p 2 a s -1 a v z -1 c -1 p 2 a s -1 a v z -1 α 4 b s c -1 p -1 2 a s a v z -1 α Gamma α c -1 p -1 2 a s a v z -1 -1 c -1 p -1 2 a s a v z -1 α Gamma α -1 c -1 p -1 2 a s a v z 2 b v c -1 p 2 a s -1 a v z -1 α Gamma α c -1 p 2 a s -1 a v z v SuperPlus [/itex]

 Rule Form

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

 2002-12-18