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Cot






Mathematica Notation

Traditional Notation









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





http://functions.wolfram.com/01.09.21.0250.01









  


  










Input Form





Integrate[(Cot[t] - 1/t) (z - t)^n, {t, 0, z}] == z^n (Log[Sin[z]] - Log[z]) - (I n z^(1 + n))/(1 + n) - z^n Sum[((-1)^(n - j) Binomial[n, j])/(n - j), {j, 0, n - 1}] - Sum[(-1)^(n - j) Binomial[n, j] z^j Sum[(Binomial[n - j, k] k! z^(n - j - k) PolyLog[k + 1, E^(-2 I z)])/ (2 I)^k, {k, 0, n - j}], {j, 0, n - 1}] + Sum[Binomial[n, j] (-2 I)^(j - n) (n - j)! z^j PolyLog[1 + n - j, 1], {j, 0, n - 1}] /; 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)





2007-05-02