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 Cosh

 http://functions.wolfram.com/01.20.21.4627.01

 Input Form

 Integrate[E^(b z^r + e) Sinh[a z^r + q] Cosh[c z^r + g]^v, z] == (-((I 2^(-1 - v) z)/r)) (Binomial[v, v/2] ((E^(e - (I Pi)/2 + q) Gamma[1/r, (-a - b) z^r])/ ((-a - b) z^r)^r^(-1) + (E^(e + (I Pi)/2 - q) Gamma[1/r, (a - b) z^r])/ ((a - b) z^r)^r^(-1)) (1 - Mod[v, 2]) + Sum[Binomial[v, s] ((E^(e - (I Pi)/2 + q - 2 g s + g v) Gamma[1/r, (-a - b + 2 c s - c v) z^r])/((-a - b + 2 c s - c v) z^r)^ r^(-1) + (E^(e + (I Pi)/2 - q - 2 g s + g v) Gamma[1/r, (a - b + 2 c s - c v) z^r])/((a - b + 2 c s - c v) z^r)^ r^(-1) + (E^(e - (I Pi)/2 + q + 2 g s - g v) Gamma[1/r, (-a - b - 2 c s + c v) z^r])/((-a - b - 2 c s + c v) z^r)^ r^(-1) + (E^(e + (I Pi)/2 - q + 2 g s - g v) Gamma[1/r, (a - b - 2 c s + c v) z^r])/((a - b - 2 c s + c v) z^r)^ r^(-1)), {s, 0, Floor[(1/2) (-1 + v)]}]) /; Element[v, Integers] && v > 0

 Standard Form

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 MathML Form

 b z r + e sinh ( a z r + q ) cosh v ( c z r + g ) z - 2 - v - 1 z r ( ( 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]]]]] ( e + q - π 2 Γ ( 1 r , ( - a - b ) z r ) ( ( - a - b ) z r ) - 1 / r + e - q + π 2 ( ( a - b ) z r ) - 1 / r Γ ( 1 r , ( a - b ) z r ) ) ( 1 - v mod 2 \$CellContext`v 2 ) + 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]]]]] ( e + q + 2 g s - g v - π 2 Γ ( 1 r , ( - a - b - 2 c s + c v ) z r ) ( ( - a - b - 2 c s + c v ) z r ) - 1 / r + e - q + 2 g s - g v + π 2 ( ( a - b - 2 c s + c v ) z r ) - 1 / r Γ ( 1 r , ( a - b - 2 c s + c v ) z r ) + e + q - 2 g s + g v - π 2 ( ( - a - b + 2 c s - c v ) z r ) - 1 / r Γ ( 1 r , ( - a - b + 2 c s - c v ) z r ) + e - q - 2 g s + g v + π 2 ( ( a - b + 2 c s - c v ) z r ) - 1 / r Γ ( 1 r , ( a - b + 2 c s - c v ) z r ) ) ) /; v + Condition z b z r e a z r q c z r g v -1 2 -1 v -1 z r -1 Binomial v v 2 -1 e q -1 2 -1 Gamma 1 r -1 -1 a -1 b z r -1 a -1 b z r -1 r -1 e -1 q 2 -1 a -1 b z r -1 r -1 Gamma 1 r -1 a -1 b z r 1 -1 \$CellContext`v 2 s 0 v -1 2 -1 Binomial v s e q 2 g s -1 g v -1 2 -1 Gamma 1 r -1 -1 a -1 b -1 2 c s c v z r -1 a -1 b -1 2 c s c v z r -1 r -1 e -1 q 2 g s -1 g v 2 -1 a -1 b -1 2 c s c v z r -1 r -1 Gamma 1 r -1 a -1 b -1 2 c s c v z r e q -1 2 g s g v -1 2 -1 -1 a -1 b 2 c s -1 c v z r -1 r -1 Gamma 1 r -1 -1 a -1 b 2 c s -1 c v z r e -1 q -1 2 g s g v 2 -1 a -1 b 2 c s -1 c v z r -1 r -1 Gamma 1 r -1 a -1 b 2 c s -1 c v z r v SuperPlus [/itex]

 Rule Form

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

 2002-12-18