Re: lambertW2

On Dec 27, 9:42 am, "I.N. Galidakis" <morph...@xxxxxxxxxxxx> wrote:
tommy1729 wrote:
z= lambertW2(z)* exp( exp (lambertW2(z)) )

in other words lambertW2(z) is the inverse of z*exp(exp(z))

No it's not.

The principal branch of the inverse of z*exp(exp(z)) is real-valued for example
in [0,+oo).

W(2,x) is complex valued there.

The inverse of z*exp(exp(z)) cannot be expressed in terms of the Lambert W
function.

a nice function ...

i suspect he was defining a "second" lambert-like function
not using the common lambert w here

lagrange inversion gives a power series
with lots of e's in the terms
though

-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
galathaea: prankster, fablist, magician, liar
.

Relevant Pages

  • Re: Solution of Transcendental Equation: Exp(a.X) + b.X + c
    ... monir writes: ... one using the principal branch and the other using ... So we've established that the value of Lambert function W ... has the series expansion: ...
    (sci.math)
  • Re: lambertW2
    ... galathaea wrote: ... The principal branch of the inverse of z*exp) is real-valued ... Lambert W function. ... I thought that by lambertW2he meant the second branch of the ...
    (sci.math)
  • Re: How to solve this natural log problem?
    ... On 30 Jan 2007 23:20:30 GMT, David W. Cantrell ... Their W0 computes the principal branch of the Lambert W function, ...
    (sci.math)
  • Re: Solution of Transcendental Equation: Exp(a.X) + b.X + c
    ... one using the principal branch and the other ... The 32-term series expansion ... Lambert Function W can reasonably be approximated by few terms. ... I've tried with no success to access the reference provided by David: ...
    (sci.math)
  • Re: How to solve this natural log problem?
    ... Dirk has objected to mentioning the Lambert W function in responses to ... Their W0 computes the principal branch of the Lambert W function, ...
    (sci.math)