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1: 10.74 Methods of Computation
Furthermore, the attainable accuracy can be increased substantially by use of the exponentially-improved expansions given in §10.17(v), even more so by application of the hyperasymptotic expansions to be found in the references in that subsection. …
2: 2.11 Remainder Terms; Stokes Phenomenon
For other examples see Boyd (1990b), Paris (1992a, b), and Wong and Zhao (2002b). … In this way we arrive at hyperasymptotic expansions. …
3: 13.29 Methods of Computation
However, this accuracy can be increased considerably by use of the exponentially-improved forms of expansion supplied by the combination of (13.7.10) and (13.7.11), or by use of the hyperasymptotic expansions given in Olde Daalhuis and Olver (1995a). …
4: 13.7 Asymptotic Expansions for Large Argument
For extensions to hyperasymptotic expansions see Olde Daalhuis and Olver (1995a).
5: Bibliography P
  • R. B. Paris (2001a) On the use of Hadamard expansions in hyperasymptotic evaluation. I. Real variables. Proc. Roy. Soc. London Ser. A 457 (2016), pp. 2835–2853.
  • R. B. Paris (2001b) On the use of Hadamard expansions in hyperasymptotic evaluation. II. Complex variables. Proc. Roy. Soc. London Ser. A 457, pp. 2855–2869.
  • 6: Bibliography O
  • A. B. Olde Daalhuis and F. W. J. Olver (1995a) Hyperasymptotic solutions of second-order linear differential equations. I. Methods Appl. Anal. 2 (2), pp. 173–197.
  • A. B. Olde Daalhuis (1995) Hyperasymptotic solutions of second-order linear differential equations. II. Methods Appl. Anal. 2 (2), pp. 198–211.
  • A. B. Olde Daalhuis (1998a) Hyperasymptotic solutions of higher order linear differential equations with a singularity of rank one. Proc. Roy. Soc. London Ser. A 454, pp. 1–29.
  • A. B. Olde Daalhuis (2005a) Hyperasymptotics for nonlinear ODEs. I. A Riccati equation. Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci. 461 (2060), pp. 2503–2520.
  • A. B. Olde Daalhuis (2005b) Hyperasymptotics for nonlinear ODEs. II. The first Painlevé equation and a second-order Riccati equation. Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci. 461 (2062), pp. 3005–3021.
  • 7: Bibliography H
  • P. I. Hadži (1976a) Expansions for the probability function in series of Čebyšev polynomials and Bessel functions. Bul. Akad. Štiince RSS Moldoven. 1976 (1), pp. 77–80, 96 (Russian).
  • R. A. Handelsman and J. S. Lew (1970) Asymptotic expansion of Laplace transforms near the origin. SIAM J. Math. Anal. 1 (1), pp. 118–130.
  • R. A. Handelsman and J. S. Lew (1971) Asymptotic expansion of a class of integral transforms with algebraically dominated kernels. J. Math. Anal. Appl. 35 (2), pp. 405–433.
  • F. E. Harris (2000) Spherical Bessel expansions of sine, cosine, and exponential integrals. Appl. Numer. Math. 34 (1), pp. 95–98.
  • C. J. Howls (1992) Hyperasymptotics for integrals with finite endpoints. Proc. Roy. Soc. London Ser. A 439, pp. 373–396.
  • 8: Bibliography B
  • C. B. Balogh (1967) Asymptotic expansions of the modified Bessel function of the third kind of imaginary order. SIAM J. Appl. Math. 15, pp. 1315–1323.
  • B. C. Berndt and R. J. Evans (1984) Chapter 13 of Ramanujan’s second notebook: Integrals and asymptotic expansions. Expo. Math. 2 (4), pp. 289–347.
  • M. V. Berry and C. J. Howls (1991) Hyperasymptotics for integrals with saddles. Proc. Roy. Soc. London Ser. A 434, pp. 657–675.
  • R. Bo and R. Wong (1994) Uniform asymptotic expansion of Charlier polynomials. Methods Appl. Anal. 1 (3), pp. 294–313.
  • J. Brüning (1984) On the asymptotic expansion of some integrals. Arch. Math. (Basel) 42 (3), pp. 253–259.
  • 9: Bibliography M
  • A. J. MacLeod (1993) Chebyshev expansions for modified Struve and related functions. Math. Comp. 60 (202), pp. 735–747.
  • A. J. MacLeod (2002a) Asymptotic expansions for the zeros of certain special functions. J. Comput. Appl. Math. 145 (2), pp. 261–267.
  • J. P. McClure and R. Wong (1978) Explicit error terms for asymptotic expansions of Stieltjes transforms. J. Inst. Math. Appl. 22 (2), pp. 129–145.
  • H. J. W. Müller (1966c) On asymptotic expansions of ellipsoidal wave functions. Math. Nachr. 32, pp. 157–172.
  • B. T. M. Murphy and A. D. Wood (1997) Hyperasymptotic solutions of second-order ordinary differential equations with a singularity of arbitrary integer rank. Methods Appl. Anal. 4 (3), pp. 250–260.