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 Cosh

 http://functions.wolfram.com/01.20.21.4824.01

 Input Form

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

 Standard Form

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 MathML Form

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

 Rule Form

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

 2002-12-18