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variants of this functions
ProductLog






Mathematica Notation

Traditional Notation









Elementary Functions > ProductLog[k,z] > Integral representations > On the real axis > Of the direct function





http://functions.wolfram.com/01.32.07.0001.01









  


  










Input Form





ProductLog[k, z] == 1 + (2 I Pi k + Log[z] - 1) Exp[(I/(2 Pi)) Integrate[(1/(1 + t)) Log[(Log[z] + t - Log[t] + (2 k - 1) I Pi)/(Log[z] + t - Log[t] + (2 k + 1) I Pi)], {t, 0, Infinity}]] /; Element[k, Integers] && !IntervalMemberQ[Interval[{-(1/E), 0}], z]










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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