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 Exp

 http://functions.wolfram.com/01.03.21.0714.01

 Input Form

 Integrate[z^(n + 1/2) (E^(c z))^\[Mu] (E^(a z))^\[Nu], z] == (-E^((-z) (c \[Mu] + a \[Nu]))) (E^(a z))^\[Nu] (E^(c z))^\[Mu] z^(3/2 + n) ((-z) (c \[Mu] + a \[Nu]))^(-(3/2) - n) (Erfc[Sqrt[(-z) (c \[Mu] + a \[Nu])]] Gamma[3/2 + n] + E^(z (c \[Mu] + a \[Nu])) Sum[((-z) (c \[Mu] + a \[Nu]))^(1/2 + j)/ Pochhammer[3/2 + n, j - n], {j, 0, n}] - E^(z (c \[Mu] + a \[Nu])) Sum[((-z) (c \[Mu] + a \[Nu]))^(1/2 + j)/Pochhammer[3/2 + n, j - n], {j, 1 + n, -1}]) /; Element[n, Integers]

 Standard Form

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 MathML Form

 z n + 1 2 ( c z ) μ ( a z ) ν z - - z ( c μ + a ν ) ( a z ) ν ( c z ) μ z n + 3 2 ( - z ( c μ + a ν ) ) - n - 3 2 ( erfc ( - z ( c μ + a ν ) ) Γ ( n + 3 2 ) + z ( c μ + a ν ) j = 0 n ( - z ( c μ + a ν ) ) j + 1 2 ( n + 3 2 ) j - n TagBox[SubscriptBox[RowBox[List["(", RowBox[List["n", "+", FractionBox["3", "2"]]], ")"]], RowBox[List["j", "-", "n"]]], Pochhammer] - z ( c μ + a ν ) j = n + 1 - 1 ( - z ( c μ + a ν ) ) j + 1 2 ( n + 3 2 ) j - n TagBox[SubscriptBox[RowBox[List["(", RowBox[List["n", "+", FractionBox["3", "2"]]], ")"]], RowBox[List["j", "-", "n"]]], Pochhammer] ) /; n TagBox["\[DoubleStruckCapitalZ]", Function[Integers]] Condition z z n 1 2 c z μ a z ν -1 -1 z c μ a ν a z ν c z μ z n 3 2 -1 z c μ a ν -1 n -1 3 2 Erfc -1 z c μ a ν 1 2 Gamma n 3 2 z c μ a ν j 0 n -1 z c μ a ν j 1 2 Pochhammer n 3 2 j -1 n -1 -1 z c μ a ν j n 1 -1 -1 z c μ a ν j 1 2 Pochhammer n 3 2 j -1 n -1 n [/itex]

 Rule Form

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

 2002-12-18