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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 zned z(ec zr+g)nu





http://functions.wolfram.com/01.03.21.0668.01









  


  










Input Form





Integrate[z^n E^(d z) (E^(c Sqrt[z] + g))^\[Nu], z] == (2^(-1 - 2 n) (E^(g + c Sqrt[z]))^\[Nu] Sum[(-1)^(-h + k) 4^k (c \[Nu])^(-h - k + 2 n) (2 d Sqrt[z] + c \[Nu])^ (h + k) (-((2 d Sqrt[z] + c \[Nu])^2/d))^((1/2) (-1 - h - k)) Binomial[k, h] Binomial[n, k] (c \[Nu] (2 d Sqrt[z] + c \[Nu]) Gamma[(1/2) (1 + h + k), -((2 d Sqrt[z] + c \[Nu])^2/(4 d))] + 2 d Sqrt[-((2 d Sqrt[z] + c \[Nu])^2/d)] Gamma[(1/2) (2 + h + k), -((2 d Sqrt[z] + c \[Nu])^2/(4 d))]), {k, 0, n}, {h, 0, k}])/ (d^(2 (1 + n)) E^((c \[Nu] (4 d Sqrt[z] + c \[Nu]))/(4 d))) /; Element[n, Integers] && n >= 0










Standard Form





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MathML Form







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</ci> </apply> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <ci> d </ci> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <ci> d </ci> <apply> <ci> Gamma </ci> <apply> <times /> <cn type='rational'> 1 <sep /> 2 </cn> <apply> <plus /> <ci> h </ci> <ci> k </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <power /> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <ci> d </ci> </apply> <apply> <times /> <ci> c </ci> <ci> &#957; </ci> </apply> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 4 </cn> <ci> d </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </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





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