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Exp






Mathematica Notation

Traditional Notation









Elementary Functions > Exp[z] > Integration > Indefinite integration > Involving functions of the direct function and a power function > Involving products of powers of the direct function and a power function > Involving product of powers of two direct functions and a power function > Involving zn(eb zr+e)mu (ec zr+f z)nu





http://functions.wolfram.com/01.03.21.0755.01









  


  










Input Form





Integrate[z^n (E^(b z^2 + e))^\[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^(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







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Rule Form





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





2002-12-18