According to Wikipedia, the Beta distribution is related to the gamma distribution by the following relation:
$$\lim_{n\to\infty}n B(k, n) = \Gamma(k, 1)$$
Can you point me to a derivation of this fact? Can it be generalized? For example, is there a similar relation that results in something other than a constant 1 for the Gamma second parameter? What if we have
$$\lim_{n\to\infty,m\to\infty,n=mb}n B(k, m) $$
That is, the two variables go to infinity while maintaining a constant ratio b.
The reason I'm asking is because I'm trying to figure out how to simplify a hieraerchical bayesian model involving the beta distribution.
(This is my first post; sorry for the math notation, the MathJaX syntax was too daunting, but I'll try to learn)