Lambert W-1 function - Printable Version +- HP Forums (https://www.hpmuseum.org/forum) +-- Forum: HP Calculators (and very old HP Computers) (/forum-3.html) +--- Forum: HP Prime (/forum-5.html) +--- Thread: Lambert W-1 function (/thread-17047.html) 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)