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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+d z)mu (ec zr+f z+g)nu





http://functions.wolfram.com/01.03.21.0767.01









  


  










Input Form





Integrate[z^n (E^(b z^2 + d z))^\[Mu] (E^(c z^2 + f z + g))^\[Nu], z] == (-(1/(2 Sqrt[b \[Mu] + c \[Nu]]))) E^(-((d \[Mu] + f \[Nu])^2/(4 (b \[Mu] + c \[Nu]))) - z (d \[Mu] + f \[Nu] + b \[Mu] z + c \[Nu] z)) (E^(z (d + b z)))^\[Mu] (E^(g + z (f + c z)))^\[Nu] Sum[2^(-n + q) (b \[Mu] + c \[Nu])^(-(1/2) - n) ((-d) \[Mu] - f \[Nu])^ (n - q) (d \[Mu] + f \[Nu] + 2 (b \[Mu] + c \[Nu]) z)^(1 + q) (-((d \[Mu] + f \[Nu] + 2 (b \[Mu] + c \[Nu]) z)^2/(b \[Mu] + c \[Nu])))^ ((1/2) (-1 - q)) Binomial[n, q] Gamma[(1 + q)/2, -((d \[Mu] + f \[Nu] + 2 (b \[Mu] + c \[Nu]) z)^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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</ci> </apply> <apply> <times /> <ci> f </ci> <ci> &#957; </ci> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <plus /> <apply> <times /> <ci> b </ci> <ci> &#956; </ci> </apply> <apply> <times /> <ci> c </ci> <ci> &#957; </ci> </apply> </apply> <ci> z </ci> </apply> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 4 </cn> <apply> <plus /> <apply> <times /> <ci> b </ci> <ci> &#956; </ci> </apply> <apply> <times /> <ci> c </ci> <ci> &#957; </ci> </apply> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <in /> <ci> n </ci> <ci> &#8469; </ci> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





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





2002-12-18