Stokes%20line
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1: 2.11 Remainder Terms; Stokes Phenomenon
§2.11 Remainder Terms; Stokes Phenomenon
… ►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.2: 36.5 Stokes Sets
§36.5 Stokes Sets
►§36.5(i) Definitions
… ►§36.5(ii) Cuspoids
… ►Elliptic Umbilic Stokes Set (Codimension three)
… ►§36.5(iv) Visualizations
…3: Bibliography D
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Recherches analytiques sur la théorie des nombres premiers. Première partie. La fonction de Riemann et les nombres premiers en général, suivi d’un Appendice sur des réflexions applicables à une formule donnée par Riemann.
Ann. Soc. Sci. Bruxelles 20, pp. 183–256 (French).
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Recherches analytiques sur la théorie des nombres premiers. Deuxième partie. Les fonctions de Dirichlet et les nombres premiers de la forme linéaire
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Ann. Soc. Sci. Bruxelles 20, pp. 281–397 (French).
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Complex zeros of cylinder functions.
Math. Comp. 20 (94), pp. 215–222.
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Uniform asymptotic expansions for Whittaker’s confluent hypergeometric functions.
SIAM J. Math. Anal. 20 (3), pp. 744–760.
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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.
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