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variants of this functions
Log






Mathematica Notation

Traditional Notation









Elementary Functions > Log[z] > Integration > Definite integration > Involving the direct function





http://functions.wolfram.com/01.04.21.0072.01









  


  










Input Form





Integrate[t^n Log[2 Sin[t/2]]^m, {t, 0, 2 Pi}] == Limit[Limit[(2 Pi D[D[(E^(Pi I \[Nu]) Gamma[\[Mu] + 1])/ (Gamma[\[Mu]/2 + \[Nu] + 1] Gamma[\[Mu]/2 - \[Nu] + 1]), {\[Nu], n}], {\[Mu], m}])/E^((1/2) (Pi I n)), \[Mu] -> 0], \[Nu] -> 0] /; Element[m, Integers] && m >= 0 && 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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