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Exp




Mathematica Notation

Traditional Notation









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





http://functions.wolfram.com/01.03.21.0799.01









  


  








Input Form





Integrate[t/((1 + t^2)^(k + 1) (E^(2 Pi q t) - 1)), {t, 0, Infinity}] == -(1/(4 k)) - Binomial[2 k, k]/(2^(2 k + 2) q) + (1/(k 2^(2 k))) Sum[((-1)^(j + 1)/(j - 1)!) Binomial[2 k - j - 1, k - j] 2^(j - 1) q^j PolyGamma[j, q], {j, 1, k}] /; Element[k, Integers] && Re[q] > 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)





2002-12-18