Lambert W1 function

06042021, 01:36 PM
Post: #1




Lambert W1 function  
06042021, 01:50 PM
(This post was last modified: 06182021 07:21 AM by Stevetuc.)
Post: #2




RE: Lambert W1 function
(06042021 01:36 PM)robmio Wrote: Is there a "HP PRIME" calculation program that calculates the lower branch of the Lambert W function: W1? Search on Lambertw in the hp prime software library. That program can return both branch's Edit: example lmb(0.1) returns [−3.57715206396,−0.111832559159] 

06172021, 10:21 PM
Post: #3




RE: Lambert W1 function
A good guess for e^W(x,1) is 2*x^2 , where x = [1/e, 0]
We can setup Newton's method to get e^W(x,1): > X := −0.1 > 2*X*X → 0.02 > (X+Ans)/(1+LN(Ans)), then Enter, Enter, Enter ... 2.74723104353ᴇ−2 2.79535734165ᴇ−2 2.79551995963ᴇ−2 2.79551996147ᴇ−2 // = e^W(0.1,1) > LN(Ans), or X/Ans −3.57715206396 // = W(0.1,1) Or, Newton's method straight for W(x,1), solving f(w) = w + ln(w/x) = 0 > LN(2*X*X) → −3.91202300543 > LN(e*X/Ans)*Ans/(Ans+1), then Enter, Enter, Enter ... −3.58237415547 −3.57715353929 −3.57715206396 // = W(0.1,1) 

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