I'm currently working on a problem, which involves Poisson-Binomial Distribution. https://en.wikipedia.org/wiki/Poisson_binomial_distribution . The Mean of PBD is given by $M=\sum_{i=1}^{n}p_i$ .Probability term is of the form $p_i=\frac{1}{1+(X-1)e^{-iCX}}$. In my work $p_i$ is the probability that a person is infected from a particular epidemic disease at time $i$ among $X$ samples.
$M=\sum_i^n\frac{1}{{1+(X-1)e^{-iCX}}}$. Where $C$ is a constant.Can we approximate M to give a single expression? I am finding it difficult because of the exponent term in the denominator. Any hints or references would be of great help.
