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 Cosh

 http://functions.wolfram.com/01.20.21.3989.01

 Input Form

 Integrate[z^n E^(b Sqrt[z] + e) Cos[a Sqrt[z] + q] Cosh[c Sqrt[z] + g]^v, z] == (-2^(-v)) 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]) - Sum[Binomial[v, k] ((E^(e + I q + g (-2 k + v)) Gamma[2 (1 + n), ((-I) a - b - c (-2 k + v)) Sqrt[z]])/((-I) a - b - c (-2 k + v))^ (2 (1 + n)) + (E^(e - I q + g (-2 k + v)) Gamma[2 (1 + n), (I a - b - c (-2 k + v)) Sqrt[z]])/(I a - b - c (-2 k + v))^ (2 (1 + n)) + (E^(e + I q - g (-2 k + v)) Gamma[2 (1 + n), ((-I) a - b + c (-2 k + v)) Sqrt[z]])/((-I) a - b + c (-2 k + v))^ (2 (1 + n)) + (E^(e - I q - g (-2 k + v)) Gamma[2 (1 + n), (I a - b + c (-2 k + v)) Sqrt[z]])/(I a - b + c (-2 k + v))^ (2 (1 + n))), {k, 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 cos ( 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 Γ ( 2 ( n + 1 ) , ( - b - a ) z ) ( - b - a ) - 2 ( n + 1 ) + ( a - b ) - 2 ( n + 1 ) e - q Γ ( 2 ( n + 1 ) , ( a - b ) z ) ) ( 1 - v mod 2 \$CellContext`v 2 ) - 2 - v k = 0 v - 1 2 ( v k ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["v", Identity]], List[TagBox["k", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] ( e + q - g ( v - 2 k ) Γ ( 2 ( n + 1 ) , ( - b - a + c ( v - 2 k ) ) z ) ( - b - a + c ( v - 2 k ) ) - 2 ( n + 1 ) + e - q - g ( v - 2 k ) ( - b + a + c ( v - 2 k ) ) - 2 ( n + 1 ) Γ ( 2 ( n + 1 ) , ( - b + a + c ( v - 2 k ) ) z ) + e + q + g ( v - 2 k ) ( - b - a - c ( v - 2 k ) ) - 2 ( n + 1 ) Γ ( 2 ( n + 1 ) , ( - b - a - c ( v - 2 k ) ) z ) + e - q + g ( v - 2 k ) ( - b + a - c ( v - 2 k ) ) - 2 ( n + 1 ) Γ ( 2 ( n + 1 ) , ( - b + a - c ( v - 2 k ) ) z ) ) /; v + n Condition z z n z 1 2 b e z 1 2 a q z 1 2 c g v -1 2 -1 v Binomial v v 2 -1 e q Gamma 2 n 1 -1 b -1 a z 1 2 -1 b -1 a -2 n 1 a -1 b -2 n 1 e -1 q Gamma 2 n 1 a -1 b z 1 2 1 -1 \$CellContext`v 2 -1 2 -1 v k 0 v -1 2 -1 Binomial v k e q -1 g v -1 2 k Gamma 2 n 1 -1 b -1 a c v -1 2 k z 1 2 -1 b -1 a c v -1 2 k -2 n 1 e -1 q -1 g v -1 2 k -1 b a c v -1 2 k -2 n 1 Gamma 2 n 1 -1 b a c v -1 2 k z 1 2 e q g v -1 2 k -1 b -1 a -1 c v -1 2 k -2 n 1 Gamma 2 n 1 -1 b -1 a -1 c v -1 2 k z 1 2 e -1 q g v -1 2 k -1 b a -1 c v -1 2 k -2 n 1 Gamma 2 n 1 -1 b a -1 c v -1 2 k z 1 2 v SuperPlus n [/itex]

 Rule Form

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

 2002-12-18