asymptotic approximations and expansions
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1: 14.26 Uniform Asymptotic Expansions
§14.26 Uniform Asymptotic Expansions
…2: 18.29 Asymptotic Approximations for -Hahn and Askey–Wilson Classes
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►For a uniform asymptotic expansion of the Stieltjes–Wigert polynomials, see Wang and Wong (2006).
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3: 18.24 Hahn Class: Asymptotic Approximations
§18.24 Hahn Class: Asymptotic Approximations
… ►Asymptotic approximations are also provided for the zeros of in various cases depending on the values of and . … ►For asymptotic approximations for the zeros of in terms of zeros of (§9.9(i)), see Jin and Wong (1999) and Khwaja and Olde Daalhuis (2012). … ►Approximations in Terms of Laguerre Polynomials
… ►Similar approximations are included for Jacobi, Krawtchouk, and Meixner polynomials.4: 18.32 OP’s with Respect to Freud Weights
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►However, for asymptotic approximations in terms of elementary functions for the OP’s, and also for their largest zeros, see Levin and Lubinsky (2001) and Nevai (1986).
For a uniform asymptotic expansion in terms of Airy functions (§9.2) for the OP’s in the case see Bo and Wong (1999).
►For asymptotic approximations to OP’s that correspond to Freud weights with more general functions see Deift et al. (1999a, b), Bleher and Its (1999), and Kriecherbauer and McLaughlin (1999).
5: 28.26 Asymptotic Approximations for Large
§28.26 Asymptotic Approximations for Large
►§28.26(i) Goldstein’s Expansions
… ►The asymptotic expansions of and in the same circumstances are also given by the right-hand sides of (28.26.4) and (28.26.5), respectively. … ►§28.26(ii) Uniform Approximations
… ►For asymptotic approximations for see also Naylor (1984, 1987, 1989).6: 2.1 Definitions and Elementary Properties
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►means that for each , the difference between and the th partial sum on the right-hand side is as in .
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►Some asymptotic approximations are expressed in terms of two or more Poincaré asymptotic expansions.
…For an example see (2.8.15).
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