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 Cosh

 http://functions.wolfram.com/01.20.21.0384.01

 Input Form

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

 Standard Form

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 MathML Form

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

 Rule Form

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

 2002-12-18