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 Cosh

 http://functions.wolfram.com/01.20.21.1449.01

 Input Form

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

 Standard Form

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 MathML Form

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

 Rule Form

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

 2002-12-18