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variants of this functions
Erf






Mathematica Notation

Traditional Notation









Gamma, Beta, Erf > Erf[z] > Integration > Indefinite integration > Involving one direct function and elementary functions > Involving exponential function and a power function > Involving exp and power





http://functions.wolfram.com/06.25.21.0016.01









  


  










Input Form





Integrate[z^n E^(b z) Erf[a z], z] == (-(-b)^(-1 - n)) Gamma[1 + n, (-b) z] Erf[a z] - (-b)^(-1 - n) (a/Sqrt[Pi]) n! E^(b^2/(4 a^2)) Sum[((-b)^m/m!) (-a^2)^((1/2) (-1 - m)) Sum[Binomial[m, k] (-(b/(2 Sqrt[-a^2])))^(m - k) (Sqrt[-a^2] z + b/(2 Sqrt[-a^2]))^(1 + k) (-(Sqrt[-a^2] z + b/(2 Sqrt[-a^2]))^2)^((1/2) (-1 - k)) Gamma[(1 + k)/2, -(Sqrt[-a^2] z + b/(2 Sqrt[-a^2]))^2], {k, 0, m}], {m, 0, n}] /; Element[n, Integers] && n >= 0










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)





2001-10-29