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Erfi




Mathematica Notation

Traditional Notation









Gamma, Beta, Erf > Erfi[z] > Integration > Indefinite integration > Involving direct function and Gamma-, Beta-, Erf-type functions > Involving erf-type functions and a power function > Involving erfc and power





http://functions.wolfram.com/06.28.21.0139.01









  


  








Input Form





Integrate[z^(\[Alpha] - 1) Erfc[a z] Erfi[a z], z] == (z^\[Alpha]/(2 \[Alpha])) (2 Erfi[a z] + ((2 a z)/(((-a^2) z^2)^((\[Alpha] + 1)/2) Sqrt[Pi])) Gamma[(1 + \[Alpha])/2, (-a^2) z^2] - ((8 a^2 z^2)/Pi) HypergeometricPFQ[{1/2, 1}, {3/4, 5/4, 3/2}, (a^4 z^4)/4] + Sqrt[2] a^2 z^2 Gamma[(2 + \[Alpha])/4] HypergeometricPFQRegularized[ {1, (2 + \[Alpha])/4}, {3/4, 5/4, (6 + \[Alpha])/4}, (a^4 z^4)/4])








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