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 Cosh

 http://functions.wolfram.com/01.20.21.0360.01

 Input Form

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

 Standard Form

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 MathML Form

 z n b z 2 + e cosh ( c z ) z - 1 4 b - n - 1 e - c 2 4 b ( q = 0 n 2 q - n c n - q ( 2 b z - c ) q + 1 ( - ( 2 b z - c ) 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 , - ( 2 b z - c ) 2 4 b ) + q = 0 n 2 q - n ( - c ) n - q ( c + 2 b z ) q + 1 ( - ( c + 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 + 2 b z ) 2 4 b ) ) /; n Condition z z n b z 2 e c z -1 1 4 b -1 n -1 e -1 c 2 4 b -1 q 0 n 2 q -1 n c n -1 q 2 b z -1 c q 1 -1 2 b z -1 c 2 b -1 1 2 -1 q -1 Binomial n q Gamma q 1 2 -1 -1 2 b z -1 c 2 4 b -1 q 0 n 2 q -1 n -1 c n -1 q c 2 b z q 1 -1 c 2 b z 2 b -1 1 2 -1 q -1 Binomial n q Gamma q 1 2 -1 -1 c 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