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 Cosh

 http://functions.wolfram.com/01.20.21.3929.01

 Input Form

 Integrate[z^n E^(b Sqrt[z] + e) Sin[a Sqrt[z] + q] Cosh[c Sqrt[z] + g]^v, z] == (I Binomial[v, v/2] ((E^(e + I q) Gamma[2 (1 + n), ((-I) a - b) Sqrt[z]])/ (I a + b)^(2 (1 + n)) - (E^(e - I q) Gamma[2 (1 + n), (I a - b) Sqrt[z]])/(I a - b)^(2 (1 + n))) (1 - Mod[v, 2]))/2^v + (I Sum[Binomial[v, s] ((E^(e + I q - 2 g s + g v) Gamma[2 (1 + n), ((-I) a - b + 2 c s - c v) Sqrt[z]])/((-I) a - b + 2 c s - c v)^ (2 (1 + n)) - (E^(e - I q - 2 g s + g v) Gamma[2 (1 + n), (I a - b + 2 c s - c v) Sqrt[z]])/(I a - b + 2 c s - c v)^ (2 (1 + n)) + (E^(e + I q + 2 g s - g v) Gamma[2 (1 + n), ((-I) a - b - 2 c s + c v) Sqrt[z]])/((-I) a - b - 2 c s + c v)^ (2 (1 + n)) - (E^(e - I q + 2 g s - g v) Gamma[2 (1 + n), (I a - b - 2 c s + c v) Sqrt[z]])/(I a - b - 2 c s + c 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 sin ( 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]]]]] ( e + q ( b + a ) - 2 ( n + 1 ) Γ ( 2 ( n + 1 ) , ( - b - a ) z ) - e - q ( a - b ) - 2 ( n + 1 ) 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 + 2 g s - g v Γ ( 2 ( n + 1 ) , ( - b - a - 2 c s + c v ) z ) ( - b - a - 2 c s + c v ) - 2 ( n + 1 ) - e - q + 2 g s - g v ( - b + a - 2 c s + c v ) - 2 ( n + 1 ) Γ ( 2 ( n + 1 ) , ( - b + a - 2 c s + c v ) z ) + e + q - 2 g s + g v ( - b - a + 2 c s - c v ) - 2 ( n + 1 ) Γ ( 2 ( n + 1 ) , ( - b - a + 2 c s - c v ) z ) - e - q - 2 g s + g v ( - b + a + 2 c s - c v ) - 2 ( n + 1 ) Γ ( 2 ( n + 1 ) , ( - b + a + 2 c s - c v ) 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 e q b a -2 n 1 Gamma 2 n 1 -1 b -1 a z 1 2 -1 e -1 q a -1 b -2 n 1 Gamma 2 n 1 a -1 b z 1 2 1 -1 \$CellContext`v 2 2 -1 v s 0 v -1 2 -1 Binomial v s e q 2 g s -1 g v Gamma 2 n 1 -1 b -1 a -1 2 c s c v z 1 2 -1 b -1 a -1 2 c s c v -2 n 1 -1 e -1 q 2 g s -1 g v -1 b a -1 2 c s c v -2 n 1 Gamma 2 n 1 -1 b a -1 2 c s c v z 1 2 e q -1 2 g s g v -1 b -1 a 2 c s -1 c v -2 n 1 Gamma 2 n 1 -1 b -1 a 2 c s -1 c v z 1 2 -1 e -1 q -1 2 g s g v -1 b a 2 c s -1 c v -2 n 1 Gamma 2 n 1 -1 b a 2 c s -1 c v z 1 2 v SuperPlus n [/itex]

 Rule Form

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

 2002-12-18