# Solve problem with the lambert W function?

Posted 9 months ago
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 I have facing a problem in solving the lambert W function in mathematica. I have generated the x values from lambert function but I cant get the solution .ProductLog", \[Phi] = 0.5; \[Kappa] = 0.2; u = RandomReal[ {0, 1}, 10]; x = (1/\[Phi])* Log[(\[Kappa] - 1 + ((1 + \[Kappa])^2 - 4*\[Kappa]*u)^0.5)/( 2*\[Kappa])] - (1/\[Phi]^2) - (1/\[Phi])*\!$$\* ButtonBox["ProductLog", BaseStyle->"Link", ButtonData->"paclet:ref/ProductLog"]$$[-(1/\[Phi])* Exp[-(1/\[Phi])] ((\[Kappa] - 1 + ((1 + \[Kappa])^2 - 4*\[Kappa]*u)^0.5)/(2*\[Kappa]))] 
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Posted 9 months ago
 This is not comprehensible (and the subject title is meaningless). What exactly is wanted? Something like this? In[27]:= phi = 0.5; kap = 0.2; u = RandomReal[{0, 1}, 10]; x = (1/phi)* Log[(kap - 1 + ((1 + kap)^2 - 4 kap u)^0.5)/(2 kap)] - (1/ phi^2) - (1/phi) Out[27]= {-7.50006616149, -6.17473673094, -9.36459249618, \ -8.78032746892, -9.33316651726, -9.80992590354, -6.29708140172, \ -6.01196696005, -6.34504903014, -6.70520204079} In[28]:= ProductLog[(1/phi)* Exp[-(1/phi)] ((kap - 1 + ((1 + kap)^2 - 4 kap u)^0.5)/(2*kap))] Out[28]= {0.114068677509, 0.202549549343, 0.0479727646523, \ 0.063273418175, 0.0486972217016, 0.0387521917698, 0.192462165763, \ 0.216647476984, 0.188623734815, 0.161819558864} 
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