Some Useful Integral Asymptotic Expansions The following lemmas

A.1. Some Useful Integral Asymptotic Expansions The following lemmas provide results on asymptotic expansions of integrals that are useful in the main arguments. In particular, these results are used to develop bias expansions for the binding function bn(ρ) (see equation (14) of the paper) for three separate fixed ρ cases (|ρ| < 1, ρ = ±1, and |ρ| > 1) and to show asymptotic behavior in the local to unity case where ρ= 1 + c n for fixed c and for |c| → ∞ with c = o(n) as n → ∞. These integral asymptotic expansion formulae are likely to have applications in other contexts.