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 Cosh

 http://functions.wolfram.com/01.20.21.1410.01

 Input Form

 Integrate[z^n E^(p z) Cos[b z^2] Cosh[c z], z] == (-(I/(8 b))) ((Sqrt[(-I) b] Sum[2^(-n + q) ((-I) b)^(-(1/2) - n) (-c - p)^(n - q) (c + p - 2 I b z)^(1 + q) (-((I (c + p - 2 I b z)^2)/b))^((1/2) (-1 - q)) Binomial[n, q] Gamma[(1 + q)/2, -((I (c + p - 2 I b z)^2)/(4 b))], {q, 0, n}] + Sqrt[(-I) b] E^((I c p)/b) Sum[2^(-n + q) ((-I) b)^(-(1/2) - n) (c - p)^(n - q) (-c + p - 2 I b z)^(1 + q) (-((I (c - p + 2 I b z)^2)/b))^((1/2) (-1 - q)) Binomial[n, q] Gamma[(1 + q)/2, -((I (c - p + 2 I b z)^2)/(4 b))], {q, 0, n}] - Sqrt[I b] (E^((I (c^2 + p^2))/(2 b)) Sum[2^(-n + q) (I b)^(-(1/2) - n) (c - p)^(n - q) (-c + p + 2 I b z)^(1 + q) ((I (-c + p + 2 I b z)^2)/b)^((1/2) (-1 - q)) Binomial[n, q] Gamma[(1 + q)/2, (I (-c + p + 2 I b z)^2)/(4 b)], {q, 0, n}] + E^((I (c + p)^2)/(2 b)) Sum[2^(-n + q) (I b)^(-(1/2) - n) (-c - p)^(n - q) (c + p + 2 I b z)^(1 + q) ((I (c + p + 2 I b z)^2)/b)^((1/2) (-1 - q)) Binomial[n, q] Gamma[(1 + q)/2, (I (c + p + 2 I b z)^2)/(4 b)], {q, 0, n}]))/ E^((I (c + p)^2)/(4 b))) /; Element[n, Integers] && n >= 0

 Standard Form

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 MathML Form

 z n p z cos ( b z 2 ) cosh ( c z ) z - 8 b - ( c + p ) 2 4 b ( - b ( ( c 2 + p 2 ) 2 b q = 0 n 2 q - n ( b ) - n - 1 2 ( c - p ) n - q ( - c + p + 2 b z ) q + 1 ( ( - c + p + 2 b z ) 2 b ) 1 2 ( - q - 1 ) ( n q ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["n", Identity]], List[TagBox["q", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] Γ ( q + 1 2 , ( - c + p + 2 b z ) 2 4 b ) + ( c + p ) 2 2 b q = 0 n 2 q - n ( b ) - n - 1 2 ( - c - p ) n - q ( c + p + 2 b z ) q + 1 ( ( c + p + 2 b z ) 2 b ) 1 2 ( - q - 1 ) ( n q ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["n", Identity]], List[TagBox["q", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] Γ ( q + 1 2 , ( c + p + 2 b z ) 2 4 b ) ) + - b c p b q = 0 n 2 q - n ( - b ) - n - 1 2 ( c - p ) n - q ( - c + p - 2 b z ) q + 1 ( - ( c - p + 2 b z ) 2 b ) 1 2 ( - q - 1 ) ( n q ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["n", Identity]], List[TagBox["q", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] Γ ( q + 1 2 , - ( c - p + 2 b z ) 2 4 b ) + - b q = 0 n 2 q - n ( - b ) - n - 1 2 ( - c - p ) n - q ( c + p - 2 b z ) q + 1 ( - ( c + p - 2 b z ) 2 b ) 1 2 ( - q - 1 ) ( n q ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["n", Identity]], List[TagBox["q", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] Γ ( q + 1 2 , - ( c + p - 2 b z ) 2 4 b ) ) /; n Condition z z n p z b z 2 c z -1 8 b -1 -1 c p 2 4 b -1 -1 b 1 2 c 2 p 2 2 b -1 q 0 n 2 q -1 n b -1 n -1 1 2 c -1 p n -1 q -1 c p 2 b z q 1 -1 c p 2 b z 2 b -1 1 2 -1 q -1 Binomial n q Gamma q 1 2 -1 -1 c p 2 b z 2 4 b -1 c p 2 2 b -1 q 0 n 2 q -1 n b -1 n -1 1 2 -1 c -1 p n -1 q c p 2 b z q 1 c p 2 b z 2 b -1 1 2 -1 q -1 Binomial n q Gamma q 1 2 -1 c p 2 b z 2 4 b -1 -1 b 1 2 c p b -1 q 0 n 2 q -1 n -1 b -1 n -1 1 2 c -1 p n -1 q -1 c p -1 2 b z q 1 -1 c -1 p 2 b z 2 b -1 1 2 -1 q -1 Binomial n q Gamma q 1 2 -1 -1 c -1 p 2 b z 2 4 b -1 -1 b 1 2 q 0 n 2 q -1 n -1 b -1 n -1 1 2 -1 c -1 p n -1 q c p -1 2 b z q 1 -1 c p -1 2 b z 2 b -1 1 2 -1 q -1 Binomial n q Gamma q 1 2 -1 -1 c p -1 2 b z 2 4 b -1 n [/itex]

 Rule Form

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

 2002-12-18