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1: Bibliography T
  • N. M. Temme (1990a) Asymptotic estimates for Laguerre polynomials. Z. Angew. Math. Phys. 41 (1), pp. 114–126.
  • N. M. Temme (1993) Asymptotic estimates of Stirling numbers. Stud. Appl. Math. 89 (3), pp. 233–243.
  • 2: 27.2 Functions
    27.2.3 π ( x ) x ln x .
    3: 1.8 Fourier Series
    Asymptotic Estimates of Coefficients
    4: Bibliography L
  • D. J. Leeming (1977) An asymptotic estimate for the Bernoulli and Euler numbers. Canad. Math. Bull. 20 (1), pp. 109–111.
  • 5: 26.8 Set Partitions: Stirling Numbers
    For asymptotic estimates for generalized Stirling numbers see Chelluri et al. (2000). …
    6: Bibliography C
  • R. Chelluri, L. B. Richmond, and N. M. Temme (2000) Asymptotic estimates for generalized Stirling numbers. Analysis (Munich) 20 (1), pp. 1–13.
  • 7: 27.12 Asymptotic Formulas: Primes
    The best available asymptotic error estimate (2009) appears in Korobov (1958) and Vinogradov (1958): there exists a positive constant d such that …
    8: 5.4 Special Values and Extrema
    5.4.20 x n = - n + 1 π arctan ( π ln n ) + O ( 1 n ( ln n ) 2 ) .
    9: 35.9 Applications
    For applications of the integral representation (35.5.3) see McFarland and Richards (2001, 2002) (statistical estimation of misclassification probabilities for discriminating between multivariate normal populations). The asymptotic approximations of §35.7(iv) are applied in numerous statistical contexts in Butler and Wood (2002). In chemistry, Wei and Eichinger (1993) expresses the probability density functions of macromolecules in terms of generalized hypergeometric functions of matrix argument, and develop asymptotic approximations for these density functions. …
    10: 13.29 Methods of Computation
    For large | z | the asymptotic expansions of §13.7 should be used instead. … In the sector | ph z | < 1 2 π the integration has to be towards the origin, with starting values computed from asymptotic expansions (§§13.7 and 13.19). … and estimateand estimate
    13.29.8 w ( n ) π e 1 2 z z 1 4 ( 4 a - 2 b + 1 ) Γ ( a ) Γ ( a + 1 - b ) n 1 4 ( 4 a - 2 b - 3 ) e - 2 n z ,