asymptotic approximations and expansions
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§14.26 Uniform Asymptotic Expansions…
… ►For a uniform asymptotic expansion of the Stieltjes–Wigert polynomials, see Wang and Wong (2006). …
§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.
… ►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).
§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).
… ►means that for each , the difference between and the th partial sum on the right-hand side is as in . … ►Some asymptotic approximations are expressed in terms of two or more Poincaré asymptotic expansions. …For an example see (2.8.15). … ►