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asymptotic approximations and expansions for large |r|

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11: Bibliography B
  • 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.
  • N. Bleistein and R. A. Handelsman (1975) Asymptotic Expansions of Integrals. Holt, Rinehart, and Winston, New York.
  • 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.
  • W. G. C. Boyd (1995) Approximations for the late coefficients in asymptotic expansions arising in the method of steepest descents. Methods Appl. Anal. 2 (4), pp. 475–489.
  • 12: 10.21 Zeros
    §10.21(vi) McMahon’s Asymptotic Expansions for Large Zeros
    §10.21(vii) Asymptotic Expansions for Large Order
    §10.21(viii) Uniform Asymptotic Approximations for Large Order
    The asymptotic expansion of the large positive zeros (not necessarily the m th) of the function …
    13: 30.16 Methods of Computation
    For small | γ 2 | we can use the power-series expansion (30.3.8). …If | γ 2 | is large we can use the asymptotic expansions in §30.9. Approximations to eigenvalues can be improved by using the continued-fraction equations from §30.3(iii) and §30.8; see Bouwkamp (1947) and Meixner and Schäfke (1954, §3.93). … If | γ 2 | is large, then we can use the asymptotic expansions referred to in §30.9 to approximate Ps n m ( x , γ 2 ) . … A fourth method, based on the expansion (30.8.1), is as follows. …
    14: 11.6 Asymptotic Expansions
    §11.6 Asymptotic Expansions
    §11.6(i) Large | z | , Fixed ν
    §11.6(ii) Large | ν | , Fixed z
    More fully, the series (11.2.1) and (11.2.2) can be regarded as generalized asymptotic expansions2.1(v)). …