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11: 3.4 Differentiation
The choice r = k is motivated by saddle-point analysis; see §2.4(iv) or examples in §3.5(ix). …
12: Bibliography C
  • A. Ciarkowski (1989) Uniform asymptotic expansion of an integral with a saddle point, a pole and a branch point. Proc. Roy. Soc. London Ser. A 426, pp. 273–286.
  • 13: 2.11 Remainder Terms; Stokes Phenomenon
    For large ρ the integrand has a saddle point at t = e i θ . …
    14: 36.5 Stokes Sets
    The distribution of real and complex critical points in Figures 36.5.5 and 36.5.6 follows from consistency with Figure 36.5.1 and the fact that there are four real saddles in the inner regions. …
    15: 36.7 Zeros
    The zeros in Table 36.7.1 are points in the 𝐱 = ( x , y ) plane, where ph Ψ 2 ( 𝐱 ) is undetermined. …
    16: Bibliography H
  • J. H. Hubbard and B. B. Hubbard (2002) Vector Calculus, Linear Algebra, and Differential Forms: A Unified Approach. 2nd edition, Prentice Hall Inc., Upper Saddle River, NJ.
  • C. Hunter and B. Guerrieri (1981) The eigenvalues of Mathieu’s equation and their branch points. Stud. Appl. Math. 64 (2), pp. 113–141.
  • M. N. Huxley (2003) Exponential sums and lattice points. III. Proc. London Math. Soc. (3) 87 (3), pp. 591–609.