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11: DLMF Project News
error generating summary
12: 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).
  • 13: 2.4 Contour Integrals
    However, for the purpose of simply deriving the asymptotic expansions the use of steepest descent paths is not essential. …
    14: 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)). …
    15: 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. …
    16: 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. …
    17: Errata
  • Table 18.3.1

    There has been disagreement about the identification of the Chebyshev polynomials of the third and fourth kinds, denoted V n ( x ) and W n ( x ) , in published references. Originally, DLMF used the definitions given in (Andrews et al., 1999, Remark 2.5.3). However, those definitions were the reverse of those used by Mason and Handscomb (2003), Gautschi (2004) following Mason (1993) and Gautschi (1992), as was noted in several warnings added in Version 1.0.10 (August 7, 2015) of the DLMF. Since the latter definitions are more widely established, the DLMF is now adopting the definitions of Mason and Handscomb (2003). Essentially, what we previously denoted V n ( x ) is now written as W n ( x ) , and vice-versa.

    This notational interchange necessitated changes in Tables 18.3.1, 18.5.1, and 18.6.1, and in Equations (18.5.3), (18.5.4), (18.7.5), (18.7.6), (18.7.17), (18.7.18), (18.9.11), and (18.9.12).