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1: 29.16 Asymptotic Expansions
Hargrave and Sleeman (1977) give asymptotic approximations for Lamé polynomials and their eigenvalues, including error bounds. …
2: Bibliography N
  • G. Nemes (2013b) Error bounds and exponential improvement for Hermite’s asymptotic expansion for the gamma function. Appl. Anal. Discrete Math. 7 (1), pp. 161–179.
  • G. Nemes (2014) Error bounds and exponential improvement for the asymptotic expansion of the Barnes G -function. Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci. 470 (2172), pp. 20140534, 14.
  • G. Nemes (2015a) Error bounds and exponential improvements for the asymptotic expansions of the gamma function and its reciprocal. Proc. Roy. Soc. Edinburgh Sect. A 145 (3), pp. 571–596.
  • G. Nemes (2017) Error Bounds for the Large-Argument Asymptotic Expansions of the Hankel and Bessel Functions. Acta Appl. Math. 150, pp. 141–177.
  • 3: Bibliography O
  • F. W. J. Olver and F. Stenger (1965) Error bounds for asymptotic solutions of second-order differential equations having an irregular singularity of arbitrary rank. J. Soc. Indust. Appl. Math. Ser. B Numer. Anal. 2 (2), pp. 244–249.
  • F. W. J. Olver (1964b) Error bounds for asymptotic expansions in turning-point problems. J. Soc. Indust. Appl. Math. 12 (1), pp. 200–214.
  • F. W. J. Olver (1974) Error bounds for stationary phase approximations. SIAM J. Math. Anal. 5 (1), pp. 19–29.
  • F. W. J. Olver (1976) Improved error bounds for second-order differential equations with two turning points. J. Res. Nat. Bur. Standards Sect. B 80B (4), pp. 437–440.
  • F. W. J. Olver (1980a) Asymptotic approximations and error bounds. SIAM Rev. 22 (2), pp. 188–203.
  • 4: 10.17 Asymptotic Expansions for Large Argument
    §10.17(iii) Error Bounds for Real Argument and Order
    §10.17(iv) Error Bounds for Complex Argument and Order
    Corresponding error bounds for (10.17.3) and (10.17.4) are obtainable by combining (10.17.13) and (10.17.14) with (10.4.4). … For higher re-expansions of the remainder terms see Olde Daalhuis and Olver (1995a) and Olde Daalhuis (1995, 1996).
    5: 13.19 Asymptotic Expansions for Large Argument
    Error bounds and exponentially-improved expansions are derivable by combining §§13.7(ii) and 13.7(iii) with (13.14.2) and (13.14.3). …
    6: 34.8 Approximations for Large Parameters
    For approximations for the 3 j , 6 j , and 9 j symbols with error bounds see Flude (1998), Chen et al. (1999), and Watson (1999): these references also cite earlier work.
    7: 13.7 Asymptotic Expansions for Large Argument
    §13.7(ii) Error Bounds
    Corresponding error bounds for (13.7.2) can be constructed by combining (13.2.41) with (13.7.4)–(13.7.9). …
    8: 5.11 Asymptotic Expansions
    §5.11(ii) Error Bounds and Exponential Improvement
    For error bounds for (5.11.8) and an exponentially-improved extension, see Nemes (2013b). … For further information see Olver (1997b, pp. 293–295), and for other error bounds see Whittaker and Watson (1927, §12.33), Spira (1971), and Schäfke and Finsterer (1990). … For realistic error bounds in (5.11.14) see Frenzen (1987, 1992). …
    9: 10.40 Asymptotic Expansions for Large Argument
    §10.40(ii) Error Bounds for Real Argument and Order
    §10.40(iii) Error Bounds for Complex Argument and Order
    10: Bibliography F
  • C. L. Frenzen and R. Wong (1985b) A uniform asymptotic expansion of the Jacobi polynomials with error bounds. Canad. J. Math. 37 (5), pp. 979–1007.
  • C. L. Frenzen (1987) Error bounds for asymptotic expansions of the ratio of two gamma functions. SIAM J. Math. Anal. 18 (3), pp. 890–896.
  • C. L. Frenzen (1990) Error bounds for a uniform asymptotic expansion of the Legendre function Q n - m ( cosh z ) . SIAM J. Math. Anal. 21 (2), pp. 523–535.
  • C. L. Frenzen (1992) Error bounds for the asymptotic expansion of the ratio of two gamma functions with complex argument. SIAM J. Math. Anal. 23 (2), pp. 505–511.