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 Cosh

 http://functions.wolfram.com/01.20.21.4825.01

 Input Form

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

 Standard Form

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 MathML Form

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

 Rule Form

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

 2002-12-18