PorductLog

[lucas_php]

How do I can typing this formula on excel?

http://functions.wolfram.com/ElementaryFunctions/ProductLog2/06/01/

Does'nt matter wha

 

[lucas_php]

http://functions.wolfram.com/ElementaryFunctions/ProductLog/06/01/02/0001/

This formula is easy, but the [Ellipsis] its difficult:

-1 + sqrt(sqrt(2)*sqrt(exp(z)+1)) - ((sqrt(sqrt(2)*sqrt(exp(z)+1))/3)
(11/72)*(sqrt(sqrt(2)*sqrt(exp(z)+1)^(2/3) + [Ellipsis]

the Ellipsis I don't know I do

(Sorry my english LoL

 

[Bernard Liengme]

I would put z in a separte cell A1
I would put e(z) in a separate column, say A2
And have cell (A3) for p
A1: =(some numerical value)
A2=EXP(A1)
A3 =SQRT(2)*SQRT(A2+1)
For the Lambert function
A4: =-1 +sqrt(A3) - A3/3 + (11/72)*A3^(3/2)
The ellipses part means (.....) you keep adding terms until tyou get the
required precision. However the Wolfram articel does not tell how to
generate the next term in the series:
p/3, (11/72)p^(3/2), ...
This articel might help http://en.wikipedia.org/wiki/Lambert's_W_function
best wishes