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 Cosh

 http://functions.wolfram.com/01.20.21.1412.01

 Input Form

 Integrate[z^n E^(p z) Cos[b z] Cosh[c z^2], z] == (2^(-4 - n) (-c)^(-n - 1) ((-E^((p (2 I b + 3 p))/(4 c))) Sum[(I b - p)^(n - q) ((-I) b + p - 2 c z)^(1 + q) Binomial[n, q] ExpIntegralE[(1 - q)/2, ((-I) b + p - 2 c z)^2/(4 c)], {q, 0, n}] - 2^n E^((3 p (2 I b + p))/(4 c)) Sum[(((-I) b - p)^(n - q) (I b + p - 2 c z)^(1 + q) Binomial[n, q] ExpIntegralE[(1 - q)/2, (I b + p - 2 c z)^2/(4 c)])/2^n, {q, 0, n}] + (-1)^n E^((2 b^2 + 2 I b p + p^2)/(4 c)) (2^n Sum[(((-I) b - p)^(n - q) (I b + p + 2 c z)^(1 + q) Binomial[n, q] ExpIntegralE[(1 - q)/2, -((I b + p + 2 c z)^2/(4 c))])/2^n, {q, 0, n}] + E^((I b p)/c) Sum[(I b - p)^(n - q) ((-I) b + p + 2 c z)^(1 + q) Binomial[n, q] ExpIntegralE[(1 - q)/2, (b + I (p + 2 c z))^2/(4 c)], {q, 0, n}])))/ E^((b^2 + 4 I b p + 2 p^2)/(4 c)) /; Element[n, Integers] && n >= 0

 Standard Form

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 MathML Form

 z n p z cos ( b z ) cosh ( c z 2 ) z 2 - n - 4 ( - c ) - n - 1 - b 2 + 4 p b + 2 p 2 4 c ( - p ( 2 b + 3 p ) 4 c q = 0 n ( b - p ) n - q ( - b + p - 2 c z ) q + 1 ( n q ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["n", Identity]], List[TagBox["q", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] E TagBox["E", ExpIntegralE] 1 - q 2 ( ( - b + p - 2 c z ) 2 4 c ) - 2 n 3 p ( 2 b + p ) 4 c q = 0 n 2 - n ( - b - p ) n - q ( b + p - 2 c z ) q + 1 ( n q ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["n", Identity]], List[TagBox["q", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] E TagBox["E", ExpIntegralE] 1 - q 2 ( ( b + p - 2 c z ) 2 4 c ) + ( - 1 ) n 2 b 2 + 2 p b + p 2 4 c ( b p c q = 0 n ( b - p ) n - q ( - b + p + 2 c z ) q + 1 ( n q ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["n", Identity]], List[TagBox["q", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] E TagBox["E", ExpIntegralE] 1 - q 2 ( ( b + ( p + 2 c z ) ) 2 4 c ) + 2 n q = 0 n 2 - n ( - b - p ) n - q ( b + p + 2 c z ) q + 1 ( n q ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["n", Identity]], List[TagBox["q", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] E TagBox["E", ExpIntegralE] 1 - q 2 ( - ( b + p + 2 c z ) 2 4 c ) ) ) /; n Condition z z n p z b z c z 2 2 -1 n -4 -1 c -1 n -1 -1 b 2 4 p b 2 p 2 4 c -1 -1 p 2 b 3 p 4 c -1 q 0 n b -1 p n -1 q -1 b p -1 2 c z q 1 Binomial n q ExpIntegralE 1 -1 q 2 -1 -1 b p -1 2 c z 2 4 c -1 -1 2 n 3 p 2 b p 4 c -1 q 0 n 2 -1 n -1 b -1 p n -1 q b p -1 2 c z q 1 Binomial n q ExpIntegralE 1 -1 q 2 -1 b p -1 2 c z 2 4 c -1 -1 n 2 b 2 2 p b p 2 4 c -1 b p c -1 q 0 n b -1 p n -1 q -1 b p 2 c z q 1 Binomial n q ExpIntegralE 1 -1 q 2 -1 b p 2 c z 2 4 c -1 2 n q 0 n 2 -1 n -1 b -1 p n -1 q b p 2 c z q 1 Binomial n q ExpIntegralE 1 -1 q 2 -1 -1 b p 2 c z 2 4 c -1 n [/itex]

 Rule Form

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

 2002-12-18