Complementary error function: Integration (formula 06.27.21.0133)

Erfc

$Mathematica Notation$

Gamma, Beta, Erf

Erfc[z]

Integration

Definite integration

Involving the direct function

http://functions.wolfram.com/06.27.21.0133.01

Input Form

Integrate[(t^(\[Alpha] - 1) Erfc[t])/E^(z t), {t, 0, Infinity}] == (1/Sqrt[Pi]) ((1/\[Alpha]) Gamma[(1 + \[Alpha])/2] HypergeometricPFQ[{(\[Alpha] + 1)/2, \[Alpha]/2}, {1/2, 1 + \[Alpha]/2}, z^2/4] - (z/(1 + \[Alpha])) Gamma[1 + \[Alpha]/2] HypergeometricPFQ[{(\[Alpha] + 1)/2, 1 + \[Alpha]/2}, {3/2, (3 + \[Alpha])/2}, z^2/4]) /; Re[z] > 0 && Re[\[Alpha]] > 0

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