♦ 4 matching pages ♦
4 matching pages
… ►The choice of and is facilitated by a knowledge of the relevant Stokes lines; see §2.11(iv) below. … ►Rays (or curves) on which one contribution in a compound asymptotic expansion achieves maximum dominance over another are called Stokes lines ( in the present example). … ►The relevant Stokes lines are for , and for . … ►For example, extrapolated values may converge to an accurate value on one side of a Stokes line (§2.11(iv)), and converge to a quite inaccurate value on the other.
§36.5 Stokes Sets►
§36.5(i) Definitions… ►
§36.5(ii) Cuspoids… ►
Elliptic Umbilic Stokes Set (Codimension three)… ►
8.22.1►plays a fundamental role in re-expansions of remainder terms in asymptotic expansions, including exponentially-improved expansions and a smooth interpretation of the Stokes phenomenon. … ►The function , with and , has an intimate connection with the Riemann zeta function (§25.2(i)) on the critical line . …
Bessel functions of purely imaginary order, with an application to second-order linear differential equations having a large parameter.
SIAM J. Math. Anal. 21 (4), pp. 995–1018.
Asymptotics of the generalized exponential integral, and error bounds in the uniform asymptotic smoothing of its Stokes discontinuities.
Proc. Roy. Soc. London Ser. A 452, pp. 1351–1367.