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 Cosh

 http://functions.wolfram.com/01.20.21.0999.01

 Input Form

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

 Standard Form

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 MathML Form

 z α - 1 sin m ( b z r + e ) cosh ( c z r + g ) z - 1 r ( ( - 1 ) m 2 - m - 1 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]]]]] ( g Γ ( α r , - c z r ) ( - c z r ) - α r + - g ( c z r ) - α r Γ ( α r , c z r ) ) ( 1 - m mod 2 \$CellContext`m 2 ) ) - 1 r - m 2 - m - 1 z α 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 g + 2 e k - e m Γ ( α r , ( - c - 2 b k + b m ) z r ) ( ( - c - 2 b k + b m ) z r ) - α r + ( - 1 ) m - g + 2 e k - e m ( ( c - 2 b k + b m ) z r ) - α r Γ ( α r , ( c - 2 b k + b m ) z r ) + g - 2 e k + e m ( ( - c + 2 b k - b m ) z r ) - α r Γ ( α r , ( - c + 2 b k - b m ) z r ) + - g - 2 e k + e m ( ( c + 2 b k - b m ) z r ) - α r Γ ( α r , ( c + 2 b k - b m ) z r ) ) /; m + Condition z z α -1 b z r e m c z r g -1 1 r -1 -1 m 2 -1 m -1 z α Binomial m m 2 -1 g Gamma α r -1 -1 c z r -1 c z r -1 α r -1 -1 g c z r -1 α r -1 Gamma α r -1 c z r 1 -1 \$CellContext`m 2 -1 1 r -1 -1 m 2 -1 m -1 z α k 0 m -1 2 -1 -1 k Binomial m k -1 m g 2 e k -1 e m Gamma α r -1 -1 c -1 2 b k b m z r -1 c -1 2 b k b m z r -1 α r -1 -1 m -1 g 2 e k -1 e m c -1 2 b k b m z r -1 α r -1 Gamma α r -1 c -1 2 b k b m z r g -1 2 e k e m -1 c 2 b k -1 b m z r -1 α r -1 Gamma α r -1 -1 c 2 b k -1 b m z r -1 g -1 2 e k e m c 2 b k -1 b m z r -1 α r -1 Gamma α r -1 c 2 b k -1 b m z r m SuperPlus [/itex]

 Rule Form

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

 2002-12-18