Error function: Integration (formula 06.25.21.0117)

Erf

$Mathematica Notation$

Gamma, Beta, Erf

Erf[z]

Integration

Indefinite integration

Involving one direct function and elementary functions

Involving logarithm and a power function

Involving log and power

http://functions.wolfram.com/06.25.21.0117.01

Input Form

Integrate[z Log[b z] Erf[a z], z] == (1/(36 Sqrt[Pi] (a^2 z^2)^(3/2))) (a z^3 (-9 (Sqrt[Pi] Log[z] + Gamma[3/2, a^2 z^2] (1 - 2 Log[b z])) + a z Sqrt[a^2 z^2] (4 a z HypergeometricPFQ[{3/2, 3/2}, {5/2, 5/2}, (-a^2) z^2] + 9 Sqrt[Pi] Erf[a z] (-1 + 2 Log[b z]))))

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

Erf[z₁,z₂]