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Erfc




Mathematica Notation

Traditional Notation









Gamma, Beta, Erf > Erfc[z] > Integration > Indefinite integration > Involving functions of the direct function and elementary functions > Involving elementary functions of the direct function and elementary functions > Involving powers of the direct function and a power function





http://functions.wolfram.com/06.27.21.0121.01









  


  








Input Form





Integrate[z^(\[Alpha] - 1) Erfc[a z]^2, z] == (z^\[Alpha]/\[Alpha]) (Erfc[a z]^2 - (2 a z (a^2 z^2)^((1/2) (-1 - \[Alpha])) Gamma[(1 + \[Alpha])/2, a^2 z^2])/Sqrt[Pi]) + (((4 z^\[Alpha])/(Pi \[Alpha])) Sum[((-1)^k Gamma[(\[Alpha] + 3)/2 + k, a^2 z^2])/((1 + 2 k) k!), {k, 0, Infinity}])/(a^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