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LogIntegral






Mathematica Notation

Traditional Notation









Gamma, Beta, Erf > LogIntegral[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/06.36.21.0011.01









  


  










Input Form





Integrate[z^(\[Alpha] - 1) Log[a z]^n LogIntegral[a z], z] == (z^\[Alpha]/((-\[Alpha])^n (a z)^\[Alpha] \[Alpha])) Gamma[1 + n, (-\[Alpha]) Log[a z]] LogIntegral[a z] - ((-\[Alpha])^(-n - 1) z^\[Alpha] n! Sum[(Gamma[k, (-(1 + \[Alpha])) Log[a z]] \[Alpha]^k)/ ((1 + \[Alpha])^k k!), {k, 0, n}])/(a z)^\[Alpha] /; Element[n, Integers] && n >= 0










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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