Let and be the polynomials defined in
Then as ,
uniformly for . All fractional powers take their principal
All four expansions also enjoy the same kind of double asymptotic property
described in §10.41(iv).
Accuracy in (10.69.2) and (10.69.4) can be increased by
including exponentially-small contributions as in (10.67.3),
(10.67.4), (10.67.7), and (10.67.8)
with replaced by .