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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/06.28.21.0137.01









  


  










Input Form





Integrate[z^(\[Alpha] - 1) Erfc[b z] Erfi[a z], z] == (a z^(1 + \[Alpha]) ((-a^2) z^2)^((1/2) (-1 - \[Alpha])) Gamma[(1 + \[Alpha])/2, (-a^2) z^2])/(Sqrt[Pi] \[Alpha]) + (z^\[Alpha] Erfi[a z] Erfc[b z])/\[Alpha] + (((2 b z^\[Alpha])/(Pi \[Alpha] a)) Sum[(b^(2 k) Gamma[1 + k + \[Alpha]/2, (-a^2) z^2])/ (a^(2 k) ((2 k + 1) k!)), {k, 0, Infinity}])/ ((-a^2) z^2)^(\[Alpha]/2) - (((2 a z^\[Alpha])/(Pi \[Alpha] b)) Sum[(a^(2 k) Gamma[1 + k + \[Alpha]/2, b^2 z^2])/ (b^(2 k) ((2 k + 1) k!)), {k, 0, Infinity}])/(b^2 z^2)^(\[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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