The cumulative distribution function of a random variable
X distributed according to the Poisson distribution with shape parameter
λ (the mean) has zero slope everywhere except where a jump occurs,
F(x) = P(X ≤ x), given by
F(x) = 
0  for x < 0  e^{ λ } Σ_{i=0}^{[x] } λ^{i} / i!  for 0 ≤ x  

The corresponding probability point distribution,
f(i), i = 0,..., is
f(i) = e^{ λ } λ^{i} / i!  for i = 0,..., 

 double Poisson_Cumulative_Distribution( int k, double mu )
This function returns F(k) where F(k) is described above.
 double Poisson_Point_Distribution( int n, int k, double p )
This function returns f(k) where f(k) is described above.
 void Poisson_Distribution_Tables( int size, double mu, double* pr, double* cumulative )
This function returns f(k) where f(k) is described above for k = 0,...,n in the array pr and returns F(k) where F(k) is described above for k = 0,...,n in the array cumulative.
C source code is available for these routines: