Mathematics Weblog
The LambertW Function
Friday 9 April 2004 at 2:35 pm | In Articles | 1 CommentMany equations cannot be solved exactly without using special functions. For example, to solve requires the use of the
function (or similar). This function is sometimes defined in terms of an integral from which their properties can be deduced. Thus
is defined by
and it is then clear that, for example,
There are many equations that can only be solved in terms of newly-defined functions. One such function that isn’t all that well known is the LambertW function where is defined as a solution (for
) of
. This allows you to solve equations like
which was asked about on the S.O.S. Mathematics CyberBoard
To solve let
so that
. Then
Thus and so
which is our answer.
Using tables or software this gives 1.100.
But hang on, is that the only solution? No, because for small values of
and
grows much faster than
so
for large values of
. Since both
and
are continuous on
there is another value of
for which
. A quick fiddle with a calculator gives
.
Research into the LambertW function to find out how this other solution can be given in terms of this function.
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Hi,
I want to solve an equation with the MATLAB programing language. It’s here:
I = c1*I + c2 + A1*(exp(q*(V+I*Rs)/(k*T))-1) + A2*(exp (q*(V+I*Rs)/(2*k*T))-1)
(I must find “I” )
Could you possibly help me? Is there any special command to solve it in MATLAB tools?
I must note that the ‘solve’ command didn’t work for it.
I’m looking forward to hearing the response. Please mail to me! 😉
Best wishes,
S.Imani
Comment by Somayeh — Monday 18 February 2008 8:51 am #