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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/06.27.21.0089.01









  


  










Input Form





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