1—10 of 12 matching pages
… ►For applications of the complementary error function in uniform asymptotic approximations of integrals—saddle point coalescing with a pole or saddle point coalescing with an endpoint—see Wong (1989, Chapter 7), Olver (1997b, Chapter 9), and van der Waerden (1951). ►The complementary error function also plays a ubiquitous role in constructing exponentially-improved asymptotic expansions and providing a smooth interpretation of the Stokes phenomenon; see §§2.11(iii) and 2.11(iv). …
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. …
Stokes phenomenon demystified.
Bull. Inst. Math. Appl. 31 (1-2), pp. 21–28.
Smoothing of the Stokes phenomenon for high-order differential equations.
Proc. Roy. Soc. London Ser. A 436, pp. 165–186.
Smoothing of the Stokes phenomenon using Mellin-Barnes integrals.
J. Comput. Appl. Math. 41 (1-2), pp. 117–133.
The Stokes phenomenon associated with the Hurwitz zeta function
Proc. Roy. Soc. London Ser. A 461, pp. 297–304.
§2.11 Remainder Terms; Stokes Phenomenon… ►
§2.11(iv) Stokes Phenomenon… ►That the change in their forms is discontinuous, even though the function being approximated is analytic, is an example of the Stokes phenomenon. Where should the change-over take place? Can it be accomplished smoothly? …
… ►For exponentially-improved asymptotic expansions in the same circumstances, together with smooth interpretations of the corresponding Stokes phenomenon (§§2.11(iii)–2.11(v)) see Wong and Zhao (1999b) when , and Wong and Zhao (1999a) when . …
Quasi-linear Stokes phenomenon for the second Painlevé transcendent.
Nonlinearity 16 (1), pp. 363–386.
… ►For these and other error bounds see Olver (1997b, pp. 109–112), with and replaced by ; compare (7.11.2). ►For re-expansions of the remainder terms leading to larger sectors of validity, exponential improvement, and a smooth interpretation of the Stokes phenomenon, see §§2.11(ii)–2.11(iv) and use (7.11.3). …
Essential singularity of the Painlevé function of the second kind and the nonlinear Stokes phenomenon.
Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Steklov.
(LOMI) 187, pp. 139–170 (Russian).
Quasi-linear Stokes phenomenon for the Painlevé first equation.
J. Phys. A 37 (46), pp. 11149–11167.
… ►For re-expansions of the remainder term leading to larger sectors of validity, exponential improvement, and a smooth interpretation of the Stokes phenomenon, see §§2.11(ii)–2.11(iv), with . …
10: Bibliography H
On the higher-order Stokes phenomenon.
Proc. Roy. Soc. London Ser. A 460, pp. 2285–2303.