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asymptotic behavior

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11: Bibliography N
  • V. Yu. Novokshënov (1985) The asymptotic behavior of the general real solution of the third Painlevé equation. Dokl. Akad. Nauk SSSR 283 (5), pp. 1161–1165 (Russian).
  • 12: 30.8 Expansions in Series of Ferrers Functions
    30.8.6 a n , k m ( γ 2 ) = ( n m ) ! ( n + m + 2 k ) ! ( n + m ) ! ( n m + 2 k ) ! a n , k m ( γ 2 ) .
    13: 1.8 Fourier Series
    Lebesgue Constants
    14: 2.10 Sums and Sequences
    The asymptotic behavior of entire functions defined by Maclaurin series can be approached by converting the sum into a contour integral by use of the residue theorem and applying the methods of §§2.4 and 2.5. … What is the asymptotic behavior of f n as n or n ? More specially, what is the behavior of the higher coefficients in a Taylor-series expansion? …
  • (c)

    The coefficients in the Laurent expansion

    2.10.27 g ( z ) = n = g n z n , 0 < | z | < r ,

    have known asymptotic behavior as n ± .

  • 15: 2.4 Contour Integrals
    with known asymptotic behavior as t + . … For integral representations of the b 2 s and their asymptotic behavior as s see Boyd (1995). …
    16: Bibliography K
  • A. A. Kapaev (1988) Asymptotic behavior of the solutions of the Painlevé equation of the first kind. Differ. Uravn. 24 (10), pp. 1684–1695 (Russian).
  • 17: 15.12 Asymptotic Approximations
    For the asymptotic behavior of 𝐅 ( a , b ; c ; z ) as z with a , b , c fixed, combine (15.2.2) with (15.8.2) or (15.8.8). …
    18: 8.12 Uniform Asymptotic Expansions for Large Parameter
    For the asymptotic behavior of c k ( η ) as k see Dunster et al. (1998) and Olde Daalhuis (1998c). …
    19: 25.11 Hurwitz Zeta Function
    §25.11(xii) a -Asymptotic Behavior
    20: Bibliography C
  • O. Costin (1999) Correlation between pole location and asymptotic behavior for Painlevé I solutions. Comm. Pure Appl. Math. 52 (4), pp. 461–478.