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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 hyperbolic functions and a power function > Involving cosh and power





http://functions.wolfram.com/06.27.21.0084.01









  


  










Input Form





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





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