Langlands dual of orthogonal groups

Question

The Langlands duals of the special orthogonal groups are well-known: $SO(2n+1)^{\vee}=USp(2n)$ and $SO(2n)^{\vee} = SO(2n)$.

But what are the duals of the full orthogonal groups, $O(2n+1)^{\vee}$ and $O(2n)^{\vee}$ ?