# re-expansion of remainder terms

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## 10 matching pages

##### 1: 6.12 Asymptotic Expansions

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►For these and other error bounds see Olver (1997b, pp. 109–112) with $\alpha =0$.
►For re-expansions of the remainder term leading to larger sectors of validity, exponential improvement, and a smooth interpretation of the Stokes phenomenon, see §§2.11(ii)–2.11(iv), with $p=1$.
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##### 2: 12.9 Asymptotic Expansions for Large Variable

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###### §12.9(ii) Bounds and Re-Expansions for the Remainder Terms

…##### 3: 8.22 Mathematical Applications

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►plays a fundamental role in re-expansions of remainder terms in asymptotic expansions, including exponentially-improved expansions and a smooth interpretation of the Stokes phenomenon.
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##### 4: 2.11 Remainder Terms; Stokes Phenomenon

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###### §2.11(iii) Exponentially-Improved Expansions

… ►For illustration, we give re-expansions of the remainder terms in the expansions (2.7.8) arising in differential-equation theory. … ►For example, extrapolated values may converge to an accurate value on one side of a Stokes line (§2.11(iv)), and converge to a quite inaccurate value on the other.##### 5: 7.12 Asymptotic Expansions

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►For re-expansions of the remainder terms leading to larger sectors of validity, exponential improvement, and a smooth interpretation of the Stokes phenomenon, see §§2.11(ii)–2.11(iv) and use (7.11.3).
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##### 6: 11.6 Asymptotic Expansions

##### 7: 9.7 Asymptotic Expansions

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►For re-expansions of the remainder terms in (9.7.7)–(9.7.14) combine the results of this section with those of §9.2(v) and their differentiated forms, as in §9.7(iv).
►For higher re-expansions of the remainder terms see Olde Daalhuis (1995, 1996), and Olde Daalhuis and Olver (1995a).
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##### 8: 5.11 Asymptotic Expansions

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►For re-expansions of the remainder terms in (5.11.1) and (5.11.3) in series of incomplete gamma functions with exponential improvement (§2.11(iii)) in the asymptotic expansions, see Berry (1991), Boyd (1994), and Paris and Kaminski (2001, §6.4).
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##### 9: 10.40 Asymptotic Expansions for Large Argument

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►For higher re-expansions of the remainder term see Olde Daalhuis and Olver (1995a), Olde Daalhuis (1995, 1996), and Paris (2001a, b).