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 Cosh

 http://functions.wolfram.com/01.20.21.3988.01

 Input Form

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

 Standard Form

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RowBox[List[RowBox[List["v", "\[Element]", "Integers"]], "\[And]", RowBox[List["v", ">", "0"]], "\[And]", RowBox[List["n", "\[Element]", "Integers"]], "\[And]", RowBox[List["n", "\[GreaterEqual]", "0"]]]]]]]]

 MathML Form

 z n b z 2 + e cos ( 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 Γ ( n + 1 2 , ( - b - a ) z 2 ) ( ( - b - a ) z 2 ) 1 2 ( - n - 1 ) + 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 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 ( n + 1 2 , ( - b - a + c ( v - 2 k ) ) z 2 ) ( ( - b - a + c ( v - 2 k ) ) z 2 ) 1 2 ( - n - 1 ) + e - q - g ( v - 2 k ) ( ( - b + a + c ( v - 2 k ) ) z 2 ) 1 2 ( - n - 1 ) Γ ( n + 1 2 , ( - b + a + c ( v - 2 k ) ) z 2 ) + e + q + g ( v - 2 k ) ( ( - b - a - c ( v - 2 k ) ) z 2 ) 1 2 ( - n - 1 ) Γ ( n + 1 2 , ( - b - a - c ( v - 2 k ) ) z 2 ) + e - q + g ( v - 2 k ) ( ( - b + a - c ( v - 2 k ) ) z 2 ) 1 2 ( - n - 1 ) Γ ( n + 1 2 , ( - b + a - c ( v - 2 k ) ) 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 Gamma n 1 2 -1 -1 b -1 a z 2 -1 b -1 a z 2 1 2 -1 n -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 k 0 v -1 2 -1 Binomial v k e q -1 g v -1 2 k Gamma n 1 2 -1 -1 b -1 a c v -1 2 k z 2 -1 b -1 a c v -1 2 k z 2 1 2 -1 n -1 e -1 q -1 g v -1 2 k -1 b a c v -1 2 k z 2 1 2 -1 n -1 Gamma n 1 2 -1 -1 b a c v -1 2 k z 2 e q g v -1 2 k -1 b -1 a -1 c v -1 2 k z 2 1 2 -1 n -1 Gamma n 1 2 -1 -1 b -1 a -1 c v -1 2 k z 2 e -1 q g v -1 2 k -1 b a -1 c v -1 2 k z 2 1 2 -1 n -1 Gamma n 1 2 -1 -1 b a -1 c v -1 2 k z 2 v SuperPlus n [/itex]

 Rule Form

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

 2002-12-18