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 Exp

 http://functions.wolfram.com/01.03.21.0709.01

 Input Form

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

 Standard Form

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 MathML Form

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

 Rule Form

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

 2002-12-18