Error function: Integration (formula 06.25.21.0116)

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/06.25.21.0116.01

Input Form

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

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]