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method of steepest descents

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1: Bibliography B
  • W. G. C. Boyd (1993) Error bounds for the method of steepest descents. Proc. Roy. Soc. London Ser. A 440, pp. 493–518.
  • W. G. C. Boyd (1994) Gamma function asymptotics by an extension of the method of steepest descents. Proc. Roy. Soc. London Ser. A 447, pp. 609–630.
  • W. G. C. Boyd (1995) Approximations for the late coefficients in asymptotic expansions arising in the method of steepest descents. Methods Appl. Anal. 2 (4), pp. 475–489.
  • 2: 2.4 Contour Integrals
    Paths on which ( z p ( t ) ) is constant are also the ones on which | exp ( - z p ( t ) ) | decreases most rapidly. For this reason the name method of steepest descents is often used. …
    3: Bibliography P
  • R. B. Paris (2004) Exactification of the method of steepest descents: The Bessel functions of large order and argument. Proc. Roy. Soc. London Ser. A 460, pp. 2737–2759.
  • 4: 13.20 Uniform Asymptotic Approximations for Large μ
    5: Bibliography C
  • C. Chester, B. Friedman, and F. Ursell (1957) An extension of the method of steepest descents. Proc. Cambridge Philos. Soc. 53, pp. 599–611.
  • 6: 9.17 Methods of Computation
    In the first method the integration path for the contour integral (9.5.4) is deformed to coincide with paths of steepest descent2.4(iv)). …
    7: Bibliography T
  • N. M. Temme (1994c) Steepest descent paths for integrals defining the modified Bessel functions of imaginary order. Methods Appl. Anal. 1 (1), pp. 14–24.
  • 8: 3.5 Quadrature
    Stroud and Secrest (1966) includes computational methods and extensive tables. …
    §3.5(ix) Other Contour Integrals
    For example, steepest descent paths can be used; see §2.4(iv). … The steepest descent path is given by ( t - 2 t ) = 0 , or in polar coordinates t = r e i θ we have r = sec 2 ( 1 2 θ ) . … A special case is the rule for Hilbert transforms (§1.14(v)): …
    9: 5.21 Methods of Computation
    §5.21 Methods of Computation
    Another approach is to apply numerical quadrature (§3.5) to the integral (5.9.2), using paths of steepest descent for the contour. …