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 Exp

 http://functions.wolfram.com/01.03.21.0753.01

 Input Form

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

 Standard Form

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 MathML Form

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

 Rule Form

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

 2002-12-18