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 Exp

 http://functions.wolfram.com/01.03.21.0721.01

 Input Form

 Integrate[z^n (E^(c z + d))^\[Mu] (E^(a z + b))^\[Nu], z] == (-E^((-z) (c \[Mu] + a \[Nu]))) (E^(b + a z))^\[Nu] (E^(d + c z))^\[Mu] z^(1 + n) ((-z) (c \[Mu] + a \[Nu]))^(-1 - n) (((-1)^n ExpIntegralEi[z (c \[Mu] + a \[Nu])])/(-1 - n)! + E^(z (c \[Mu] + a \[Nu])) Sum[((-z) (c \[Mu] + a \[Nu]))^j/ Pochhammer[1 + n, j - n], {j, 0, n}] - E^(z (c \[Mu] + a \[Nu])) Sum[((-z) (c \[Mu] + a \[Nu]))^j/Pochhammer[1 + n, j - n], {j, 1 + n, -1}]) /; Element[n, Integers]

 Standard Form

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 MathML Form

 z n ( c z + d ) μ ( a z + b ) ν z - - z ( c μ + a ν ) ( b + a z ) ν ( d + c z ) μ z n + 1 ( - z ( c μ + a ν ) ) - n - 1 ( ( - 1 ) n Ei ( z ( c μ + a ν ) ) ( - n - 1 ) ! + z ( c μ + a ν ) j = 0 n ( - z ( c μ + a ν ) ) j ( n + 1 ) j - n TagBox[SubscriptBox[RowBox[List["(", RowBox[List["n", "+", "1"]], ")"]], RowBox[List["j", "-", "n"]]], Pochhammer] - z ( c μ + a ν ) j = n + 1 - 1 ( - z ( c μ + a ν ) ) j ( n + 1 ) j - n TagBox[SubscriptBox[RowBox[List["(", RowBox[List["n", "+", "1"]], ")"]], RowBox[List["j", "-", "n"]]], Pochhammer] ) /; n TagBox["\[DoubleStruckCapitalZ]", Function[Integers]] Condition z z n c z d μ a z b ν -1 -1 z c μ a ν b a z ν d c z μ z n 1 -1 z c μ a ν -1 n -1 -1 n ExpIntegralEi z c μ a ν -1 n -1 -1 z c μ a ν j 0 n -1 z c μ a ν j Pochhammer n 1 j -1 n -1 -1 z c μ a ν j n 1 -1 -1 z c μ a ν j Pochhammer n 1 j -1 n -1 n [/itex]

 Rule Form

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

 2002-12-18

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