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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 cosh





http://functions.wolfram.com/06.27.21.0111.01









  


  










Input Form





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










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





© 1998- Wolfram Research, Inc.