Stokes%20phenomenon
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11—20 of 112 matching pages
11: 7.12 Asymptotic Expansions
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►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).
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12: Bibliography W
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The Nahm equations, finite-gap potentials and Lamé functions.
J. Phys. A 20 (10), pp. 2679–2683.
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Smoothing of Stokes’s discontinuity for the generalized Bessel function. II.
Proc. Roy. Soc. London Ser. A 455, pp. 3065–3084.
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Smoothing of Stokes’s discontinuity for the generalized Bessel function.
Proc. Roy. Soc. London Ser. A 455, pp. 1381–1400.
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The Stokes set of the cusp diffraction catastrophe.
J. Phys. A 13 (9), pp. 2913–2928.
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13: 2.7 Differential Equations
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►in which , are constants, the so-called Stokes multipliers.
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►This phenomenon is an example of resurgence, a classification due to Écalle (1981a, b).
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►For the calculation of Stokes multipliers see Olde Daalhuis and Olver (1995b).
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14: Bibliography O
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On the calculation of Stokes multipliers for linear differential equations of the second order.
Methods Appl. Anal. 2 (3), pp. 348–367.
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On higher-order Stokes phenomena of an inhomogeneous linear ordinary differential equation.
J. Comput. Appl. Math. 169 (1), pp. 235–246.
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An error analysis of the modified Clenshaw method for evaluating Chebyshev and Fourier series.
J. Inst. Math. Appl. 20 (3), pp. 379–391.
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15: 6.12 Asymptotic Expansions
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►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 .
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16: Bibliography H
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On the higher-order Stokes phenomenon.
Proc. Roy. Soc. London Ser. A 460, pp. 2285–2303.
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17: 20 Theta Functions
Chapter 20 Theta Functions
…18: Sidebar 9.SB1: Supernumerary Rainbows
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►Airy invented his function in 1838 precisely to describe this phenomenon more accurately than Young had done in 1800 when pointing out that supernumerary rainbows require the wave theory of light and are impossible to explain with Newton’s picture of light as a stream of independent corpuscles.
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19: 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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20: Bibliography S
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Transformations of the Jacobian amplitude function and its calculation via the arithmetic-geometric mean.
SIAM J. Math. Anal. 20 (6), pp. 1514–1528.
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Uniform asymptotic forms of modified Mathieu functions.
Quart. J. Mech. Appl. Math. 20 (3), pp. 365–380.
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A Maple package for symmetric functions.
J. Symbolic Comput. 20 (5-6), pp. 755–768.
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Numerical Methods Based on Sinc and Analytic Functions.
Springer Series in Computational Mathematics, Vol. 20, Springer-Verlag, New York.
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A stable quotient-difference algorithm.
Math. Comp. 34 (150), pp. 515–519.
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