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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 power, exponential and hyperbolic functions > Involving power, exp and sinh





http://functions.wolfram.com/06.27.21.0105.01









  


  










Input Form





Integrate[(1/z) E^(b z^2) Sinh[c z^2] Erfc[a z], z] == (1/4) (-ExpIntegralEi[(b - c) z^2] + ExpIntegralEi[(b + c) z^2]) + ((a z)/(2 Sqrt[Pi])) ((1/Sqrt[(-(b + c)) z^2]) Sum[(a^(2 k) Gamma[1/2 + k, (-(b + c)) z^2])/((b + c)^k ((1 + 2 k) k!)), {k, 0, Infinity}] - (1/Sqrt[(-(b - c)) z^2]) Sum[(a^(2 k) Gamma[1/2 + k, (-(b - c)) z^2])/((b - c)^k ((1 + 2 k) k!)), {k, 0, Infinity}])










Standard Form





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MathML Form







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Rule Form





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2001-10-29





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