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11—15 of 15 matching pages

11: Bibliography K
  • A. A. Kapaev (1991) Essential singularity of the Painlevé function of the second kind and the nonlinear Stokes phenomenon. Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. (LOMI) 187, pp. 139–170 (Russian).
  • 12: 2.4 Contour Integrals
    However, for the purpose of simply deriving the asymptotic expansions the use of steepest descent paths is not essential. …
    13: 19.36 Methods of Computation
    All cases of R F , R C , R J , and R D are computed by essentially the same procedure (after transforming Cauchy principal values by means of (19.20.14) and (19.2.20)). …
    14: 32.10 Special Function Solutions
    The solution (32.10.34) is an essentially transcendental function of both constants of integration since P VI  with α = β = γ = 0 and δ = 1 2 does not admit an algebraic first integral of the form P ( z , w , w , C ) = 0 , with C a constant. …
    15: 9.13 Generalized Airy Functions
    The function on the right-hand side is recessive in the sector - ( 2 j - 1 ) π / m ph z ( 2 j + 1 ) π / m , and is therefore an essential member of any numerically satisfactory pair of solutions in this region. …