The moment problem for the P function of negative binomial states is solved. The explicit expressions for the P function are presented as an ordinary function as well as a distribution.
We present the s-parametrized quasiprobability distributions for the negative binomial states. Marked changes in the quasiprobability distributions W(\ensuremath{\alpha},\ensuremath{\epsilon},s) are exhibited by states that are close to the random-phase coherent state (\ensuremath{\epsilon}=0), as the parameter s is varied continuously from s=-1, corresponding to the Q function, to s=1, corresponding to the P function. However, states close to the thermal-noise state (\ensuremath{\epsilon}=1) exhibit the usual Gaussian-like distributions for all values of s.