Re: lambertW2

galathaea wrote:

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.

now but i called it lambertW2.

therefore the "2".



a nice function ...

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

indeed.



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

... what are you trying to imply here ?

i know we can give powerseries for it.

just as for lambertW.

but im looking for more intresting stuff.

like a closed form for nth derivative, relations between its branches , an integral representation , transformations , symmetries etc.

if any exist of course.

but they did for lambertW , so why not for this lambertW2.



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

thanks for your comment.

regards
tommy1729
.

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