By adding a second parameter, Conway and Maxwell created a new
distribution for situations where data deviate from the standard Poisson
distribution. This new distribution contains a normalization constant
expressed as an infinite sum whose summation has no known closed-form
expression. Shmueli et al. produced an approximation for this sum but
proved that it was valid only for integer values of the second parameter,
although they conjectured it was also valid for non-integers. Here we
prove their conjecture to be true and discuss for what range of parameters
the approximation can be accurately applied.