# resurgence

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## 6 matching pages

##### 1: Bibliography N

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The resurgence properties of the incomplete gamma function II.
Stud. Appl. Math. 135 (1), pp. 86–116.
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The resurgence properties of the incomplete gamma function, I.
Anal. Appl. (Singap.) 14 (5), pp. 631–677.
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##### 2: 2.7 Differential Equations

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►Note that the coefficients in the expansions (2.7.12), (2.7.13) for the “late” coefficients, that is, ${a}_{s,1}$, ${a}_{s,2}$ with $s$ large, are the “early” coefficients ${a}_{j,2}$, ${a}_{j,1}$ with $j$ small.
This phenomenon is an example of

*resurgence*, a classification due to Écalle (1981a, b). …##### 3: 10.20 Uniform Asymptotic Expansions for Large Order

##### 4: 2.11 Remainder Terms; Stokes Phenomenon

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###### §2.11(v) Exponentially-Improved Expansions (continued)

… ►However, to enjoy the resurgence property (§2.7(ii)) we often seek instead expansions in terms of the $F$-functions introduced in §2.11(iii), leaving the connection of the error-function type behavior as an implicit consequence of this property of the $F$-functions. … ►In addition to achieving uniform exponential improvement, particularly in $|\mathrm{ph}z|\le \pi $ for ${w}_{1}(z)$, and $0\le \mathrm{ph}z\le 2\pi $ for ${w}_{2}(z)$, the re-expansions (2.11.20), (2.11.21) are resurgent. …##### 5: Bibliography O

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On the resurgence properties of the uniform asymptotic expansion of the incomplete gamma function.
Methods Appl. Anal. 5 (4), pp. 425–438.
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##### 6: Bibliography H

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On the resurgence properties of the uniform asymptotic expansion of Bessel functions of large order.
Proc. Roy. Soc. London Ser. A 455, pp. 3917–3930.
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