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1: Bibliography N
  • G. Nemes (2015c) The resurgence properties of the incomplete gamma function II. Stud. Appl. Math. 135 (1), pp. 86–116.
  • G. Nemes (2016) The resurgence properties of the incomplete gamma function, I. Anal. Appl. (Singap.) 14 (5), pp. 631–677.
  • 2: 2.7 Differential Equations
    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
    For resurgence properties of the coefficients (§2.7(ii)) see Howls and Olde Daalhuis (1999). … …
    4: 2.11 Remainder Terms; Stokes Phenomenon
    §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 | ph z | π for w 1 ( z ) , and 0 ph z 2 π for w 2 ( z ) , the re-expansions (2.11.20), (2.11.21) are resurgent. …
    5: Bibliography O
  • A. B. Olde Daalhuis (1998c) On the resurgence properties of the uniform asymptotic expansion of the incomplete gamma function. Methods Appl. Anal. 5 (4), pp. 425–438.
  • 6: Bibliography H
  • C. J. Howls and A. B. Olde Daalhuis (1999) 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.