I like to know solution of below equation. $$e^{-0.0042x}(1+0.0042x)=0.032$$
I use 'WolframAlpha' and get two real solution(x=-235.259 and 1256.97).
General solution is $x=-\frac{5000}{21}(W_{n}(-\frac{4}{125e})+1)$ (n is integer)
I naively know when n=0 lambert w function give me a real value.
But when i set n=0, the answer is -235.259 but what i like to get is 1256.97.
Which value of n can give me 1256.97?
Thank you!
Most reference material of the Lambert W function will tell you that the two branches of the multi-valued function are referred to as $W_0$ and $W_{-1}$.
Wikipedia