resurgence%20properties%20of%20coefficients
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1: Bibliography N
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Reduction and evaluation of elliptic integrals.
Math. Comp. 20 (94), pp. 223–231.
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The resurgence properties of the large order asymptotics of the Anger-Weber function I.
J. Class. Anal. 4 (1), pp. 1–39.
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The resurgence properties of the large order asymptotics of the Anger-Weber function II.
J. Class. Anal. 4 (2), pp. 121–147.
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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: 20 Theta Functions
Chapter 20 Theta Functions
…3: 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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On the asymptotics for late coefficients in uniform asymptotic expansions of integrals with coalescing saddles.
Methods Appl. Anal. 7 (4), pp. 727–745.
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An error analysis of the modified Clenshaw method for evaluating Chebyshev and Fourier series.
J. Inst. Math. Appl. 20 (3), pp. 379–391.
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Asymptotic expansions of the coefficients in asymptotic series solutions of linear differential equations.
Methods Appl. Anal. 1 (1), pp. 1–13.
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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 -functions introduced in §2.11(iii), leaving the connection of the error-function type behavior as an implicit consequence of this property of the -functions. … ►In addition to achieving uniform exponential improvement, particularly in for , and for , the re-expansions (2.11.20), (2.11.21) are resurgent. … ►For example, using double precision is found to agree with (2.11.31) to 13D. …5: William P. Reinhardt
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►Reinhardt is a theoretical chemist and atomic physicist, who has always been interested in orthogonal polynomials and in the analyticity properties of the functions of mathematical physics.
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►In November 2015, Reinhardt was named Senior Associate Editor of the DLMF and Associate Editor for Chapters 20, 22, and 23.
6: 8 Incomplete Gamma and Related
Functions
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7: 28 Mathieu Functions and Hill’s Equation
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8: 8.26 Tables
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Khamis (1965) tabulates for , to 10D.
Abramowitz and Stegun (1964, pp. 245–248) tabulates for , to 7D; also for , to 6S.
Pagurova (1961) tabulates for , to 4-9S; for , to 7D; for , to 7S or 7D.
Zhang and Jin (1996, Table 19.1) tabulates for , to 7D or 8S.
9: 23 Weierstrass Elliptic and Modular
Functions
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10: 10.20 Uniform Asymptotic Expansions for Large Order
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►For (10.20.14) and further information on the coefficients see Temme (1997).
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►For resurgence properties of the coefficients (§2.7(ii)) see Howls and Olde Daalhuis (1999).
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