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variants of this functions
Erf






Mathematica Notation

Traditional Notation









Gamma, Beta, Erf > Erf[z] > Integration > Definite integration > Involving the direct function





http://functions.wolfram.com/06.25.21.0131.01









  


  










Input Form





Integrate[(t^(\[Alpha] - 1) Erf[t])/E^(z t), {t, 0, Infinity}] == Gamma[\[Alpha]]/z^\[Alpha] - (1/Sqrt[Pi]) ((1/\[Alpha]) Gamma[(1 + \[Alpha])/2] HypergeometricPFQ[ {(\[Alpha] + 1)/2, \[Alpha]/2}, {1/2, 1 + \[Alpha]/2}, z^2/4] - (z/(1 + \[Alpha])) Gamma[1 + \[Alpha]/2] HypergeometricPFQ[ {(\[Alpha] + 1)/2, 1 + \[Alpha]/2}, {3/2, (3 + \[Alpha])/2}, z^2/4]) /; Re[z] > 0 && Re[\[Alpha]] > -1










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