An approximate formula for the entropy of the negative binomial distribution

Recent theoretical developments revived the interest in charged particle multiplicities and their wide-spread parametrization, the negative binomial distribution (NBD). The central observable of the studies is the Shannon entropy of the NBD. A closed form is not known, however, there are representations with special series and integrals. In this note, we will investigate one of these and give an approximate formula for the entropy that is valid up to $\sim$20\% deviation from the exact value for extreme values of the NBD parameters.