this might be an ill defined question, but:
I have an experiment that computes the value <n/N> (where n is a random variable and N is fixed). I'm trying to compute <log(n/N)>, which due to nonlinearity of log function is not equal to log(<n/N>). In this case $n \in [0,N]$ The distribution is assumed to be Poissonian. Hence there arises my question:
Would it be possible to express ln(x) as a sum of Hermite polynomials on domain, let's say ($\epsilon$, $\infty$)? Or do you happen to know about any other way how to express log(x) as some sort of series (I know that Taylor is not going to work well, but maybe some other expansion would???)
Thanks in advance!