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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+e(ec z)nu





http://functions.wolfram.com/01.03.21.0634.01









  


  










Input Form





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










Standard Form





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MathML Form







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</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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