Stokes' phenomenon; smoothing a victorian discontinuity

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1. [1] M.V. BERRY, Uniform asymptotic smoothing of Stoke's discontinuities, Proc. Roy. Soc. Lond., A422 (1989), 7-21. Zbl0683.33004MR90h:34084
2. [2] T. POSTON and I. N. STEWART, Catastrophe theory and its applications, London, 1978. Zbl0382.58006MR58 #18535
3. [3] F. J. WRIGHT, The Stokes set of the cusp diffraction catastrophe, F. Phys., A13 (1980), 2913-2928. Zbl0514.58009MR82b:58020
4. [4] G. G. STOKES, On the discontinuity of arbitrary constants that appear as multipliers of semi-convergent series, Acta. Math., 26 (1902), 393-397, reprinted in Mathematical and Physical Papers by the late Sir George Gabriel Stokes, Cambridge University Press, 1905, vol. V, p. 283-287. Zbl33.0261.01JFM33.0261.01
5. [5] G. G. STOKES, On the discontinuity of arbitrary constants which appear in divergent developments, Trans. Camb. Phil. Soc., 10 (1864), 106-128, reprinted in Mathematical and Physical Papers... (ref. [4]), vol. IV, p. 77-109. 
6. [6] J. LARMOR (ed.), Sir George Gabriel Stokes : Memoir and Scientific Correspondence (Cambridge University Press, 1907), vol. 1, p. 62. JFM38.0024.04
7. [7] G. G. STOKES, On the critical values of the sums of periodic series, Trans. Camb. Phil. Soc., 8 (1847), 533-610, reprinted in Mathematical and Physical Papers... (ref. [4]), vol. I, p. 236-313. 
8. [8] R. B. DINGLE, Asymptotic Expansions : their Derivation and Interpretation, New York and London, Academic Press, 1973. Zbl0279.41030MR58 #17673
9. [9] M. V. BERRY and C. UPSTILL, Catastrophe optics : morphologies of caustics and their diffraction patterns, Progress in Optics, 18 (1980), 257-346. 
10. [10] G. B. AIRY, On the intensity of light in the neighbourhood of a caustic, Trans. Camb. Phil. Soc., 6 (1838), 379-403. 
11. [11] G. G. STOKES, On the numerical calculation of a class of definite integrals and infinite series, Trans. Camb. Phil. Soc., 9 (1847), 379-407, reprinted in Mathematical and Physical Papers... (ref. [4]), vol. II, p. 329-357. 
12. [12] R. BALIAN, G. PARISI and A. VOROS, Discrepancies from asymptotic series and their relation to complex classical trajectories, Phys. Rev. Lett., 41 (1978), 1141-1144. 
13. [13] J. ECALLE, Les fonctions résurgentes (3 vol.), Publ. Math. Université de Paris-Sud, 1981, and Cinq applications des fonctions résurgentes, preprint 84T62, Orsay, 1984. Zbl0499.30034

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