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 Cosh

 http://functions.wolfram.com/01.20.21.0364.01

 Input Form

 Integrate[z^n E^(b z^2) Cosh[f z + g], z] == (-(1/4)) b^(-1 - n) (E^(-(f^2/(4 b)) - g) Sum[2^(-n + q) f^(n - q) (-f + 2 b z)^(1 + q) (-((-f + 2 b z)^2/b))^((1/2) (-1 - q)) Binomial[n, q] Gamma[(1 + q)/2, -((-f + 2 b z)^2/(4 b))], {q, 0, n}] + E^(-(f^2/(4 b)) + g) Sum[2^(-n + q) (-f)^(n - q) (f + 2 b z)^(1 + q) (-((f + 2 b z)^2/b))^((1/2) (-1 - q)) Binomial[n, q] Gamma[(1 + q)/2, -((f + 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 cosh ( g + f z ) z - 1 4 b - n - 1 ( - f 2 4 b - g q = 0 n 2 q - n f n - q ( 2 b z - f ) q + 1 ( - ( 2 b z - f ) 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 - f ) 2 4 b ) + - f 2 4 b + g q = 0 n 2 q - n ( - f ) n - q ( f + 2 b z ) q + 1 ( - ( f + 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 , - ( f + 2 b z ) 2 4 b ) ) /; n Condition z z n b z 2 g f z -1 1 4 b -1 n -1 -1 f 2 4 b -1 -1 g q 0 n 2 q -1 n f n -1 q 2 b z -1 f q 1 -1 2 b z -1 f 2 b -1 1 2 -1 q -1 Binomial n q Gamma q 1 2 -1 -1 2 b z -1 f 2 4 b -1 -1 f 2 4 b -1 g q 0 n 2 q -1 n -1 f n -1 q f 2 b z q 1 -1 f 2 b z 2 b -1 1 2 -1 q -1 Binomial n q Gamma q 1 2 -1 -1 f 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