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steepest-descent paths

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1: 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. …
2: 3.5 Quadrature
§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)): …
3: 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)). …
4: 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.
  • 5: 36.5 Stokes Sets
    where j denotes a real critical point (36.4.1) or (36.4.2), and μ denotes a critical point with complex t or s , t , connected with j by a steepest-descent path (that is, a path where Φ = constant ) in complex t or ( s , t ) space. …
    6: 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. …However, for the purpose of simply deriving the asymptotic expansions the use of steepest descent paths is not essential. …