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 Cosh

 http://functions.wolfram.com/01.20.21.1104.01

 Input Form

 Integrate[z^(\[Alpha] - 1) Cos[c z]^m Cosh[a z], z] == 2^(-1 - m) Binomial[m, m/2] (((-z^\[Alpha]) Gamma[\[Alpha], (-a) z])/ ((-a) z)^\[Alpha] - (z^\[Alpha] Gamma[\[Alpha], a z])/(a z)^\[Alpha]) (1 - Mod[m, 2]) - 2^(-1 - m) z^\[Alpha] Sum[Binomial[m, k] (Gamma[\[Alpha], (-a + 2 I c k - I c m) z]/ ((-a + 2 I c k - I c m) z)^\[Alpha] + Gamma[\[Alpha], (a + 2 I c k - I c m) z]/((a + 2 I c k - I c m) z)^ \[Alpha] + Gamma[\[Alpha], (-a - 2 I c k + I c m) z]/ ((-a - 2 I c k + I c m) z)^\[Alpha] + 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 cos m ( c z ) cosh ( a z ) z 2 - m - 1 ( 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]]]]] ( - z α Γ ( α , - a z ) ( - a z ) - α - z α ( a z ) - α Γ ( α , a z ) ) ( 1 - m mod 2 \$CellContext`m 2 ) - 2 - m - 1 z α k = 0 m - 1 2 ( m k ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["m", Identity]], List[TagBox["k", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] ( 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 ) + ( ( a + 2 c k - c m ) z ) - α Γ ( α , ( a + 2 c k - c m ) z ) ) /; m + Condition z z α -1 c z m a z 2 -1 m -1 Binomial m m 2 -1 -1 z α Gamma α -1 a z -1 a z -1 α -1 z α a z -1 α Gamma α a z 1 -1 \$CellContext`m 2 -1 2 -1 m -1 z α k 0 m -1 2 -1 Binomial m k Gamma α -1 a -1 2 c k c m z -1 a -1 2 c k c m z -1 α a -1 2 c k c m z -1 α Gamma α a -1 2 c k c m z -1 a 2 c k -1 c m z -1 α Gamma α -1 a 2 c k -1 c m z a 2 c k -1 c m z -1 α Gamma α a 2 c k -1 c m z m SuperPlus [/itex]

 Rule Form

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

 2002-12-18