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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 zalpha-1(eb zr)mu (ec zr+g)nu





http://functions.wolfram.com/01.03.21.0739.01









  


  










Input Form





Integrate[z^(2 n) (E^(b z^2))^\[Mu] (E^(c z^2 + g))^\[Nu], z] == ((-(1/2)) (E^(b z^2))^\[Mu] (E^(g + c z^2))^\[Nu] z^(1 + 2 n) ((-z^2) (b \[Mu] + c \[Nu]))^((1/2) (-1 - 2 n)) (Erfc[Sqrt[(-z^2) (b \[Mu] + c \[Nu])]] Gamma[1/2 + n] + E^(z^2 (b \[Mu] + c \[Nu])) Sum[((-z^2) (b \[Mu] + c \[Nu]))^(1/2 + j)/ Pochhammer[1/2 + n, 1 + j - n], {j, 0, -1 + n}] - E^(z^2 (b \[Mu] + c \[Nu])) Sum[((-z^2) (b \[Mu] + c \[Nu]))^(1/2 + j)/ Pochhammer[1/2 + n, 1 + j - n], {j, n, -1}]))/ E^(z^2 (b \[Mu] + c \[Nu])) /; Element[n, Integers]










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





© 1998- Wolfram Research, Inc.