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 Cosh

 http://functions.wolfram.com/01.20.21.0958.01

 Input Form

 Integrate[z^(\[Alpha] - 1) Sin[c z]^m Cosh[b + a z], z] == ((-2^(-1 - m)) z^\[Alpha] Binomial[m, m/2] ((E^(2 b) Gamma[\[Alpha], (-a) z])/((-a) z)^\[Alpha] + Gamma[\[Alpha], a z]/(a z)^\[Alpha]) (1 - Mod[m, 2]))/E^b + 2^(-1 - m) z^\[Alpha] E^(-b - (I m Pi)/2) Sum[(-1)^k Binomial[m, k] ((-((a + 2 I c k - I c m) z)^(-\[Alpha])) Gamma[\[Alpha], (a + 2 I c k - I c m) z] + E^(2 b) ((-((-a + 2 I c k - I c m) z)^(-\[Alpha])) Gamma[\[Alpha], (-a + 2 I c k - I c m) z] - ((-1)^m Gamma[\[Alpha], (-a - 2 I c k + I c m) z])/ ((-a - 2 I c k + I c m) z)^\[Alpha]) - ((-1)^m Gamma[\[Alpha], (a - 2 I c k + I c m) z])/ ((a - 2 I c k + I c m) z)^\[Alpha]), {k, 0, Floor[(1/2) (-1 + m)]}] /; Element[m, Integers] && m > 0

 Standard Form

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 MathML Form

 z α - 1 sin m ( c z ) cosh ( b + a z ) z 2 - m - 1 z α - b - m π 2 k = 0 m - 1 2 ( - 1 ) k ( m k ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["m", Identity]], List[TagBox["k", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] ( - ( - 1 ) m Γ ( α , ( a - 2 c k + c m ) z ) ( ( a - 2 c k + c m ) z ) - α + 2 b ( - ( - 1 ) m Γ ( α , ( - a - 2 c k + c m ) z ) ( ( - a - 2 c k + c m ) z ) - α - ( ( - a + 2 c k - c m ) z ) - α Γ ( α , ( - a + 2 c k - c m ) z ) ) - ( ( a + 2 c k - c m ) z ) - α Γ ( α , ( a + 2 c k - c m ) z ) ) - 2 - m - 1 - b z α ( m m 2 ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["m", Identity]], List[TagBox[FractionBox["m", "2"], Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] ( 2 b Γ ( α , - a z ) ( - a z ) - α + ( a z ) - α Γ ( α , a z ) ) ( 1 - m mod 2 \$CellContext`m 2 ) /; m + Condition z z α -1 c z m b a z 2 -1 m -1 z α -1 b -1 m 2 -1 k 0 m -1 2 -1 -1 k Binomial m k -1 -1 m Gamma α a -1 2 c k c m z a -1 2 c k c m z -1 α 2 b -1 -1 m Gamma α -1 a -1 2 c k c m z -1 a -1 2 c k c m z -1 α -1 -1 a 2 c k -1 c m z -1 α Gamma α -1 a 2 c k -1 c m z -1 a 2 c k -1 c m z -1 α Gamma α a 2 c k -1 c m z -1 2 -1 m -1 -1 b z α Binomial m m 2 -1 2 b Gamma α -1 a z -1 a z -1 α a z -1 α Gamma α a z 1 -1 \$CellContext`m 2 m SuperPlus [/itex]

 Rule Form

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

 2002-12-18