Natural logarithm: Differentiation (formula 01.04.20.0009)

Log

$Mathematica Notation$

Elementary Functions

Log[z]

Differentiation

Fractional integro-differentiation

http://functions.wolfram.com/01.04.20.0009.02

Input Form

D[Log[a z^2 + b], {z, \[Alpha]}] == ((I Sqrt[a] z^(1 - \[Alpha]))/Sqrt[b]) Hypergeometric2F1Regularized[1, 1, 2 - \[Alpha], -((I Sqrt[a] z)/Sqrt[b])] - ((I Sqrt[a] z^(1 - \[Alpha]))/Sqrt[b]) Hypergeometric2F1Regularized[1, 1, 2 - \[Alpha], (I Sqrt[a] z)/Sqrt[b]] + (Log[b] + 2 I Pi Floor[(Pi - Arg[(a z)/b + 1] - Arg[b])/(2 Pi)]) (1/(z^\[Alpha] Gamma[1 - \[Alpha]]))

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

Log[a,z]