... giving a complete asymptoticexpansion of I(n, x) can be immediately read out of its proof.the electronic journal of combinatorics 7 (2000), #R50 4and, hence, for all n ≥ 9andallrealnumbersx,|I(n, ... asymptotic expansion for b(n, k)/n!forarange of k including the maximum of the b(n, k)/n!.AMS Subject Classification: 05A16, 05A15, 05A10A permutation σ =(σ(1), ,σ(n)) of [n]={1, ,n} has an ... are valid for all realnumbers t.sin t = t −t36+ a(t); |a(t)|≤t424 for all real t and a(t) ≥ 0fort ∈ [0,π]; (4)cos t =1−t22+ b(t); 0 ≤ b(t) ≤ t3 for t ∈ [0,π]; (5)and for an integer...