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Lambert W-1 function - robmio - 06-04-2021 01:36 PM
Is there a "HP PRIME" calculation program that calculates the lower branch of the Lambert W function: W-1?
see the magenta portion of the graph[attachment=9525]
RE: Lambert W-1 function - Stevetuc - 06-04-2021 01:50 PM
(06-04-2021 01:36 PM)robmio Wrote: Is there a "HP PRIME" calculation program that calculates the lower branch of the Lambert W function: W-1?
see the magenta portion of the graph
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]
RE: Lambert W-1 function - Albert Chan - 06-17-2021 10:21 PM
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)