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1: Bibliography D
  • T. M. Dunster (1986) Uniform asymptotic expansions for prolate spheroidal functions with large parameters. SIAM J. Math. Anal. 17 (6), pp. 1495–1524.
  • T. M. Dunster (1989) Uniform asymptotic expansions for Whittaker’s confluent hypergeometric functions. SIAM J. Math. Anal. 20 (3), pp. 744–760.
  • T. M. Dunster (1992) Uniform asymptotic expansions for oblate spheroidal functions I: Positive separation parameter λ . Proc. Roy. Soc. Edinburgh Sect. A 121 (3-4), pp. 303–320.
  • T. M. Dunster (1995) Uniform asymptotic expansions for oblate spheroidal functions II: Negative separation parameter λ . Proc. Roy. Soc. Edinburgh Sect. A 125 (4), pp. 719–737.
  • T. M. Dunster (2003b) Uniform asymptotic expansions for associated Legendre functions of large order. Proc. Roy. Soc. Edinburgh Sect. A 133 (4), pp. 807–827.
  • 2: Bibliography F
  • S. Farid Khwaja and A. B. Olde Daalhuis (2014) Uniform asymptotic expansions for hypergeometric functions with large parameters IV. Anal. Appl. (Singap.) 12 (6), pp. 667–710.
  • J. L. Fields (1973) Uniform asymptotic expansions of certain classes of Meijer G -functions for a large parameter. SIAM J. Math. Anal. 4 (3), pp. 482–507.
  • J. L. Fields (1983) Uniform asymptotic expansions of a class of Meijer G -functions for a large parameter. SIAM J. Math. Anal. 14 (6), pp. 1204–1253.
  • 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 and R. Wong (1988) Uniform asymptotic expansions of Laguerre polynomials. SIAM J. Math. Anal. 19 (5), pp. 1232–1248.
  • 3: Bibliography O
  • A. B. Olde Daalhuis (2003a) Uniform asymptotic expansions for hypergeometric functions with large parameters. I. Analysis and Applications (Singapore) 1 (1), pp. 111–120.
  • A. B. Olde Daalhuis (2003b) Uniform asymptotic expansions for hypergeometric functions with large parameters. II. Analysis and Applications (Singapore) 1 (1), pp. 121–128.
  • A. B. Olde Daalhuis (2010) Uniform asymptotic expansions for hypergeometric functions with large parameters. III. Analysis and Applications (Singapore) 8 (2), pp. 199–210.
  • F. W. J. Olver (1959) Uniform asymptotic expansions for Weber parabolic cylinder functions of large orders. J. Res. Nat. Bur. Standards Sect. B 63B, pp. 131–169.
  • F. W. J. Olver (1980b) Whittaker functions with both parameters large: Uniform approximations in terms of parabolic cylinder functions. Proc. Roy. Soc. Edinburgh Sect. A 86 (3-4), pp. 213–234.
  • 4: 28.8 Asymptotic Expansions for Large q
    §28.8 Asymptotic Expansions for Large q
    §28.8(ii) Sips’ Expansions
    Barrett’s Expansions
    Dunster’s Approximations
    5: 12.10 Uniform Asymptotic Expansions for Large Parameter
    §12.10 Uniform Asymptotic Expansions for Large Parameter
    §12.10(vi) Modifications of Expansions in Elementary Functions
    Modified Expansions
    6: 30.9 Asymptotic Approximations and Expansions
    §30.9 Asymptotic Approximations and Expansions
    §30.9(i) Prolate Spheroidal Wave Functions
    For uniform asymptotic expansions in terms of Airy or Bessel functions for real values of the parameters, complex values of the variable, and with explicit error bounds see Dunster (1986). … For uniform asymptotic expansions in terms of elementary, Airy, or Bessel functions for real values of the parameters, complex values of the variable, and with explicit error bounds see Dunster (1992, 1995). …
    7: Bibliography N
  • G. Nemes and A. B. Olde Daalhuis (2016) Uniform asymptotic expansion for the incomplete beta function. SIGMA Symmetry Integrability Geom. Methods Appl. 12, pp. 101, 5 pages.
  • G. Nemes (2015b) On the large argument asymptotics of the Lommel function via Stieltjes transforms. Asymptot. Anal. 91 (3-4), pp. 265–281.
  • G. Nemes (2017b) Error Bounds for the Large-Argument Asymptotic Expansions of the Hankel and Bessel Functions. Acta Appl. Math. 150, pp. 141–177.
  • G. Nemes (2018) Error bounds for the large-argument asymptotic expansions of the Lommel and allied functions. Stud. Appl. Math. 140 (4), pp. 508–541.
  • J. J. Nestor (1984) Uniform Asymptotic Approximations of Solutions of Second-order Linear Differential Equations, with a Coalescing Simple Turning Point and Simple Pole. Ph.D. Thesis, University of Maryland, College Park, MD.
  • 8: Bibliography W
  • Z. Wang and R. Wong (2002) Uniform asymptotic expansion of J ν ( ν a ) via a difference equation. Numer. Math. 91 (1), pp. 147–193.
  • R. Wong and Y.-Q. Zhao (2003) Estimates for the error term in a uniform asymptotic expansion of the Jacobi polynomials. Anal. Appl. (Singap.) 1 (2), pp. 213–241.
  • R. Wong and Y. Zhao (2004) Uniform asymptotic expansion of the Jacobi polynomials in a complex domain. Proc. Roy. Soc. London Ser. A 460, pp. 2569–2586.
  • R. Wong (1973a) An asymptotic expansion of W k , m ( z ) with large variable and parameters. Math. Comp. 27 (122), pp. 429–436.
  • R. Wong (1973b) On uniform asymptotic expansion of definite integrals. J. Approximation Theory 7 (1), pp. 76–86.
  • 9: Bibliography B
  • M. V. Berry (1989) Uniform asymptotic smoothing of Stokes’s discontinuities. Proc. Roy. Soc. London Ser. A 422, pp. 7–21.
  • N. Bleistein (1966) Uniform asymptotic expansions of integrals with stationary point near algebraic singularity. Comm. Pure Appl. Math. 19, pp. 353–370.
  • N. Bleistein (1967) Uniform asymptotic expansions of integrals with many nearby stationary points and algebraic singularities. J. Math. Mech. 17, pp. 533–559.
  • R. Bo and R. Wong (1994) Uniform asymptotic expansion of Charlier polynomials. Methods Appl. Anal. 1 (3), pp. 294–313.
  • A. A. Bogush and V. S. Otchik (1997) Problem of two Coulomb centres at large intercentre separation: Asymptotic expansions from analytical solutions of the Heun equation. J. Phys. A 30 (2), pp. 559–571.
  • 10: Bibliography K
  • M. Katsurada (2003) Asymptotic expansions of certain q -series and a formula of Ramanujan for specific values of the Riemann zeta function. Acta Arith. 107 (3), pp. 269–298.
  • S. F. Khwaja and A. B. Olde Daalhuis (2012) Uniform asymptotic approximations for the Meixner-Sobolev polynomials. Anal. Appl. (Singap.) 10 (3), pp. 345–361.
  • S. F. Khwaja and A. B. Olde Daalhuis (2013) Exponentially accurate uniform asymptotic approximations for integrals and Bleistein’s method revisited. Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci. 469 (2153), pp. 20130008, 12.
  • A. V. Kitaev and A. H. Vartanian (2004) Connection formulae for asymptotics of solutions of the degenerate third Painlevé equation. I. Inverse Problems 20 (4), pp. 1165–1206.
  • U. J. Knottnerus (1960) Approximation Formulae for Generalized Hypergeometric Functions for Large Values of the Parameters. J. B. Wolters, Groningen.