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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 the direct function and a power function > Involving products of two direct functions and a power function > Involving zalpha-1ab zrhc zr





http://functions.wolfram.com/01.03.21.0573.01









  


  










Input Form





Integrate[z^(2 n) a^(b z^2) h^(c z^2), z] == (-(1/2)) z^(1 + 2 n) ((-z^2) (b Log[a] + c Log[h]))^(-(1/2) - n) (Erfc[Sqrt[(-z^2) (b Log[a] + c Log[h])]] Gamma[1/2 + n] + a^(b z^2) h^(c z^2) Sum[((-z^2) (b Log[a] + c Log[h]))^(1/2 + j)/ Pochhammer[1/2 + n, 1 + j - n], {j, 0, -1 + n}] - a^(b z^2) h^(c z^2) Sum[((-z^2) (b Log[a] + c Log[h]))^(1/2 + j)/ Pochhammer[1/2 + n, 1 + j - n], {j, n, -1}]) /; Element[n, Integers]










Standard Form





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Rule Form





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2002-12-18





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