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LogGamma






Mathematica Notation

Traditional Notation









Gamma, Beta, Erf > LogGamma[z] > Differentiation > Fractional integro-differentiation





http://functions.wolfram.com/06.11.20.0006.01









  


  










Input Form





D[LogGamma[a z + b], {z, \[Alpha]}] == Sum[(a z)/(k Gamma[2 - \[Alpha]]) - ((a z)/(b + k)) Hypergeometric2F1Regularized[1, 1, 2 - \[Alpha], -((a z)/(b + k))] + (b/k - Log[(b + k)/k])/Gamma[1 - \[Alpha]], {k, 1, Infinity}]/ z^\[Alpha] - (a EulerGamma z^(1 - \[Alpha]))/Gamma[2 - \[Alpha]] - ((a z^(1 - \[Alpha]))/b) Hypergeometric2F1Regularized[1, 1, 2 - \[Alpha], -((a z)/b)] - (Log[b] + EulerGamma b)/(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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