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Stokes’ theorem

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1: 1.6 Vectors and Vector-Valued Functions
Stokes’s Theorem
2: 2.7 Differential Equations
w 2 ( z ) = e 2 π i μ 2 w 2 ( z e 2 π i ) + C 2 w 1 ( z ) ,
in which C 1 , C 2 are constants, the so-called Stokes multipliers. … For the calculation of Stokes multipliers see Olde Daalhuis and Olver (1995b). … For irregular singularities of nonclassifiable rank, a powerful tool for finding the asymptotic behavior of solutions, complete with error bounds, is as follows:
Liouville–Green Approximation Theorem
3: Bibliography B
  • M. V. Berry and C. J. Howls (1990) Stokes surfaces of diffraction catastrophes with codimension three. Nonlinearity 3 (2), pp. 281–291.
  • M. V. Berry and C. J. Howls (1994) Overlapping Stokes smoothings: Survival of the error function and canonical catastrophe integrals. Proc. Roy. Soc. London Ser. A 444, pp. 201–216.
  • M. V. Berry (1976) Waves and Thom’s theorem. Advances in Physics 25 (1), pp. 1–26.
  • M. V. Berry (1989) Uniform asymptotic smoothing of Stokes’s discontinuities. Proc. Roy. Soc. London Ser. A 422, pp. 7–21.
  • W. G. C. Boyd (1990b) Stieltjes transforms and the Stokes phenomenon. Proc. Roy. Soc. London Ser. A 429, pp. 227–246.