I wonder how do I show with Maple that for
p:=(x,a,b)->a*(a+x*b)^(x-1)*(exp(-(a+x*b)))/(x!);
the series
sum(p(x,a,b),x=0..infinity) assuming a>0,b<1,b>-1
converges to 1. I also tried
sum(a*(a+x*b)^(x-1)*(exp(-(a+x*b)))/(x!), x=m..infinity) assuming a>0,b<1,b>-1,a+m*b<=0
but all to no avail. For b=0, Maple shows the series converges and we have the Poisson distribution. For b in (-1,1), the (discrete) density...