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Erfc






Mathematica Notation

Traditional Notation









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





http://functions.wolfram.com/06.27.21.0115.01









  


  










Input Form





Integrate[z^(\[Alpha] - 1) Log[b z] Erfc[a z], z] == (z^\[Alpha] (a^2 z^2)^((1/2) (-1 - \[Alpha])) (-2 a z (a^2 z^2)^((1 + \[Alpha])/2) \[Alpha] HypergeometricPFQ[ {1/2 + \[Alpha]/2, 1/2 + \[Alpha]/2}, {3/2 + \[Alpha]/2, 3/2 + \[Alpha]/2}, (-a^2) z^2] + (1 + \[Alpha])^2 (Sqrt[Pi] (a^2 z^2)^((1 + \[Alpha])/2) Erfc[a z] (-1 + \[Alpha] Log[b z]) + a z (\[Alpha] Gamma[(1 + \[Alpha])/2] Log[z] + Gamma[(1 + \[Alpha])/2, a^2 z^2] (1 - \[Alpha] Log[b z])))))/(Sqrt[Pi] \[Alpha]^2 (1 + \[Alpha])^2)










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





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