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 Cosh

 http://functions.wolfram.com/01.20.21.3906.01

 Input Form

 Integrate[z^(\[Alpha] - 1) E^(p z) Sin[d + c z] Cosh[a z]^v, z] == 2^(-1 - v) z^\[Alpha] I ((Binomial[v, v/2] ((E^(2 I d) 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]))/E^(I d) - Sum[Binomial[v, s] (((-E^(2 I d)) Gamma[\[Alpha], ((-I) c - p + 2 a s - a v) z])/(((-I) c - p + 2 a s - a v) z)^ \[Alpha] + Gamma[\[Alpha], (I c - p + 2 a s - a v) z]/ ((I c - p + 2 a s - a v) z)^\[Alpha] - (E^(2 I d) Gamma[\[Alpha], ((-I) c - p - 2 a s + a v) z])/ (((-I) c - p - 2 a s + a v) z)^\[Alpha] + Gamma[\[Alpha], (I c - p - 2 a s + a v) z]/ ((I c - p - 2 a s + a v) z)^\[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 p z sin ( d + c z ) cosh v ( a z ) z 2 - v - 1 z α ( - d ( 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 - 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 ) - - d 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]]]]] ( - 2 d Γ ( α , ( - c - p + 2 a s - a v ) z ) ( ( - c - p + 2 a s - a v ) z ) - α + ( ( c - p - 2 a s + a v ) z ) - α Γ ( α , ( c - p - 2 a s + a v ) z ) - 2 d ( ( - 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 ) ) ) /; v + Condition z z α -1 p z d c z a z v 2 -1 v -1 z α -1 d Binomial v v 2 -1 2 d -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 -1 d s 0 v -1 2 -1 Binomial v s -1 2 d 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 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 2 d -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 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