  In this work in progress, we study the asymptotic behaviour of the
$p$-quantile of the Beta distribution, i.e. the quantity $q$ defined implicitly
by $\int_0^q t^{a - 1} (1 - t)^{b - 1} \text{d} t = p B (a, b)$, as a function
of the first parameter $a$. In particular, we derive asymptotic expansions of
and $q$ and its logarithm at $0$ and $\infty$. Moreover, we provide some
relations between Bell and N{\o}rlund Polynomials, a generalisation of
Bernoulli numbers. Finally, we provide Maple and Sage algorithms for computing
the terms of the asymptotic expansions.
