(28/48/50) Lambert W Function
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04-03-2023, 08:47 PM
(This post was last modified: 04-03-2023 09:15 PM by Albert Chan.)
Post: #25
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RE: (28/48/50) Lambert W Function
(04-03-2023 07:24 PM)John Keith Wrote: My program gets exact or near-exact results for all branches, but it is slower for branches other than 0 and -1. I was getting stupid. Of course you get near-exact result for other branches. For branches besides (0, -1), a ≈ -1/e is not that important, since W(-1/e) ≠ -1 With huge complex parts in the way, there is no catastrophic cancellation issues. (*) The singularity is at only at 0, not -1/e W-1 is the "hard" branch, with singularities at both places, 0 and -1/e. Plot[{Re[LambertW[-1,x]], Im[LambertW[-1,x]]}, {x,-1,1}] (*) Except for W1: lambertw(z, k) == conj(lambertw(conj(z), -k)) >>> lambertw(-.36787944+1e-99j, k=-1) mpc(real='-1.0000798057615958', imag='-3.4063941215654215e-95') >>> conj(lambertw(-.36787944-1e-99j, k=1)) mpc(real='-1.0000798057615958', imag='-3.4063941215654215e-95') |
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