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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 power of the direct function, the direct function and a power function > Involving zneb zr+d z(ec zr+f z+g)nu





http://functions.wolfram.com/01.03.21.0707.01









  


  










Input Form





Integrate[z^n E^(b z^2 + d z) (E^(c z^2 + f z + g))^\[Nu], z] == (-(1/(2 Sqrt[b + c \[Nu]]))) E^((-z) (f + c z) \[Nu] - (d + f \[Nu])^2/(4 (b + c \[Nu]))) (E^(g + z (f + c z)))^\[Nu] Sum[2^(-n + q) (b + c \[Nu])^(-(1/2) - n) (-d - f \[Nu])^(n - q) (d + f \[Nu] + 2 z (b + c \[Nu]))^(1 + q) (-((d + f \[Nu] + 2 z (b + c \[Nu]))^2/(b + c \[Nu])))^((1/2) (-1 - q)) Binomial[n, q] Gamma[(1 + q)/2, -((d + f \[Nu] + 2 z (b + c \[Nu]))^2/ (4 (b + 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





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