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 Cosh

 http://functions.wolfram.com/01.20.21.4081.01

 Input Form

 Integrate[Sinh[b z^r + e] Cosh[c z^r + g]^v, z] == 2^(-1 - v) z ((1/r) ((Binomial[v, v/2] ((E^(2 e) Gamma[1/r, (-b) z^r])/ ((-b) z^r)^r^(-1) - Gamma[1/r, b z^r]/(b z^r)^r^(-1)) (-1 + Mod[v, 2]))/E^e) - (1/r) Sum[E^(-e - 2 g s - g v) Binomial[v, s] ((E^(2 e + 2 g v) Gamma[1/r, (-b + 2 c s - c v) z^r])/ ((-b + 2 c s - c v) z^r)^r^(-1) - (E^(2 g v) Gamma[1/r, (b + 2 c s - c v) z^r])/((b + 2 c s - c v) z^r)^ r^(-1) + E^(4 g s) ((E^(2 e) Gamma[1/r, (-b - 2 c s + c v) z^r])/ ((-b - 2 c s + c v) z^r)^r^(-1) - Gamma[1/r, (b - 2 c s + c v) z^r]/((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

 sinh ( b z r + e ) cosh v ( c z r + g ) z 2 - v - 1 z ( - e ( 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 e ( - b z r ) - 1 / r Γ ( 1 r , - b z r ) - ( b z r ) - 1 / r Γ ( 1 r , b z r ) ) ( v mod 2 \$CellContext`v 2 - 1 ) r - 1 r s = 0 v - 1 2 - e - 2 g s - g v ( v s ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["v", Identity]], List[TagBox["s", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] ( 2 e + 2 g v Γ ( 1 r , ( - b + 2 c s - c v ) z r ) ( ( - b + 2 c s - c v ) z r ) - 1 / r + 4 g s ( 2 e ( ( - b - 2 c s + c v ) z r ) - 1 / r Γ ( 1 r , ( - b - 2 c s + c v ) z r ) - ( ( b - 2 c s + c v ) z r ) - 1 / r Γ ( 1 r , ( b - 2 c s + c v ) z r ) ) - 2 g v ( ( b + 2 c s - c v ) z r ) - 1 / r Γ ( 1 r , ( b + 2 c s - c v ) z r ) ) ) /; v + Condition z b z r e c z r g v 2 -1 v -1 z -1 e Binomial v v 2 -1 2 e -1 b z r -1 r -1 Gamma 1 r -1 -1 b z r -1 b z r -1 r -1 Gamma 1 r -1 b z r \$CellContext`v 2 -1 r -1 -1 1 r -1 s 0 v -1 2 -1 -1 e -1 2 g s -1 g v Binomial v s 2 e 2 g v Gamma 1 r -1 -1 b 2 c s -1 c v z r -1 b 2 c s -1 c v z r -1 r -1 4 g s 2 e -1 b -1 2 c s c v z r -1 r -1 Gamma 1 r -1 -1 b -1 2 c s c v z r -1 b -1 2 c s c v z r -1 r -1 Gamma 1 r -1 b -1 2 c s c v z r -1 2 g v b 2 c s -1 c v z r -1 r -1 Gamma 1 r -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