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variants of this functions
Log






Mathematica Notation

Traditional 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





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