#What is The Lambert W function and what are its uses?

34 messages · Page 1 of 1 (latest)

frosty merlin
#

Please explain to me

cursive lightBOT
#
  1. Wait patiently for a helper to come along.
  2. Once someone helps you, say thank you and close the thread with:
+close
  1. Feel free to nominate the person for helper of the week in #helper-nominations
  2. Do not ping the mods, unless someone is breaking the rules.
  3. If you're happy with the help you got here, and the server overall, you can contribute financially as well:
craggy adder
#

$W(xe^x) = x$

$W^{-1}(x) = xe^x$

tame sluiceBOT
#

wolfqz

563022261809053696.png
craggy adder
#

used to solve exponentials mainly

frosty merlin
#

Can you give an eg.?

#

Oh wait a sec

#

$xe^{x} - x = 0.1$

tame sluiceBOT
#

AstroVortex

958284399735111700.png
frosty merlin
#

Can we solve it using Lambert W functions?

craggy adder
#

hmmm wait

frosty merlin
#

Okie 👌

craggy adder
#

if there is one i cant see it

thorn dome
#

The Lambert W function is transcendental

frosty merlin
thorn dome
#

it cannot be expressed in terms of a finite number of algebraic operations and elementary functions.

frosty merlin
#

Oh

frosty merlin
#

@thorn dome

ocean yoke
#

Not possible

#

May be, the goal of the exercise is to show that we have an immediate upper bound of the solution

frosty merlin
#

I see

vagrant sorrel
craggy adder
#

,w xe^x - x = 0.1 exact solution

tame sluiceBOT
vagrant sorrel
#

,w x = productlog(0.1+x)

tame sluiceBOT
craggy adder
#

u got it

vagrant sorrel
#

👍

frosty merlin
#

Oh 'kay

#

Thanks @vagrant sorrel

frosty merlin
#

+close