  We discuss general one and two-loops banana diagrams with arbitrary masses on
the de Sitter spacetime by using direct methods of dS quantum field theory in
the dimensional regularization approach. In the one-loop case we also compute
the effective potential for an $O(N)$ model in $d=4$ dimension as an explicit
function of the cosmological constant $\Lambda$, both exactly and
perturbatively up to order $\Lambda$. For the two-loop case we show that the
calculation is made easy thanks to a remarkable Kallen-Lehmann formula that has
been in the literature for a while. We discuss the divergent cases at d=3 using
a contiguity formula for generalized hypergeometric functions and we extract
the dominant term at d=4 proving a general formula to deal with a divergent
hypergeometric series.
