x=ye^y solution derivation wanted

[Kevin Aylward]

Hello,

I would like the derivation to the power series solution of x=ye^y, for
y. This problem came from schumms calculus book but did not have the
derivation. I never could manage it, being a thick engineer. It has
applications to various electronic circuits, in particular a PTAT
generator.

Kevin Aylward
ke...@anasoft.co.uk
http://www.anasoft.co.uk

[Len Smiley]

In article <3890761E...@ti.com>,

Try the (Web-accessible) paper "On the Lambert W Function" by Corless,
Gonnet, Hare, Jeffrey, and Knuth. You can download it from Knuth's
Homepage, I think.

Len Smiley
>

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[Kevin Aylward]

Thanks Len ,

I had no idea that this was a studied function. Its use in electronics is
e.g. a current mirror, with a resistor in one on the transistor emitters the
equation:

I1 = i2exp(i2Rq/KT) occurs. Normally one iterates the answer or uses spice.

Kevin Aylward
ke...@anasoft.co.uk

Len Smiley <smi...@saturn.math.uaa.alaska.edu> wrote in message
news:86qglt$uus$1...@nnrp1.deja.com...

[Len Smiley]

Oops - it's at Corless' place:

http://www.apmaths.uwo.ca/~rcorless/papers/LambertW/index.html

It has the expansion you wanted, and quite a few applications.

Len

In article <86qglt$uus$1...@nnrp1.deja.com>,