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 Exp

 http://functions.wolfram.com/01.03.21.0729.01

 Input Form

 Integrate[z^(2 n) (E^(b z^2))^\[Mu] (E^(c z^2))^\[Nu], z] == ((-(1/2)) (E^(b z^2))^\[Mu] (E^(c z^2))^\[Nu] z^(1 + 2 n) ((-z^2) (b \[Mu] + c \[Nu]))^((1/2) (-1 - 2 n)) (Erfc[Sqrt[(-z^2) (b \[Mu] + c \[Nu])]] Gamma[1/2 + n] + E^(z^2 (b \[Mu] + c \[Nu])) Sum[((-z^2) (b \[Mu] + c \[Nu]))^(1/2 + j)/ Pochhammer[1/2 + n, 1 + j - n], {j, 0, -1 + n}] - E^(z^2 (b \[Mu] + c \[Nu])) Sum[((-z^2) (b \[Mu] + c \[Nu]))^(1/2 + j)/ Pochhammer[1/2 + n, 1 + j - n], {j, n, -1}]))/ E^(z^2 (b \[Mu] + c \[Nu])) /; Element[n, Integers]

 Standard Form

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 MathML Form

 z 2 n ( b z 2 ) μ ( c z 2 ) ν z - 1 2 - z 2 ( b μ + c ν ) ( b z 2 ) μ ( c z 2 ) ν z 2 n + 1 ( - z 2 ( b μ + c ν ) ) 1 2 ( - 2 n - 1 ) ( erfc ( - z 2 ( b μ + c ν ) ) Γ ( n + 1 2 ) + z 2 ( b μ + c ν ) j = 0 n - 1 ( - z 2 ( b μ + c ν ) ) j + 1 2 ( n + 1 2 ) j - n + 1 TagBox[SubscriptBox[RowBox[List["(", RowBox[List["n", "+", FractionBox["1", "2"]]], ")"]], RowBox[List["j", "-", "n", "+", "1"]]], Pochhammer] - z 2 ( b μ + c ν ) j = n - 1 ( - z 2 ( b μ + c ν ) ) j + 1 2 ( n + 1 2 ) j - n + 1 TagBox[SubscriptBox[RowBox[List["(", RowBox[List["n", "+", FractionBox["1", "2"]]], ")"]], RowBox[List["j", "-", "n", "+", "1"]]], Pochhammer] ) /; n TagBox["\[DoubleStruckCapitalZ]", Function[Integers]] Condition z z 2 n b z 2 μ c z 2 ν -1 1 2 -1 z 2 b μ c ν b z 2 μ c z 2 ν z 2 n 1 -1 z 2 b μ c ν 1 2 -2 n -1 Erfc -1 z 2 b μ c ν 1 2 Gamma n 1 2 z 2 b μ c ν j 0 n -1 -1 z 2 b μ c ν j 1 2 Pochhammer n 1 2 j -1 n 1 -1 -1 z 2 b μ c ν j n -1 -1 z 2 b μ c ν j 1 2 Pochhammer n 1 2 j -1 n 1 -1 n [/itex]

 Rule Form

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

 2002-12-18