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1: 14.26 Uniform Asymptotic Expansions

§14.26 Uniform Asymptotic Expansions

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2: 9.15 Mathematical Applications

… ►Airy functions play an indispensable role in the construction of uniform asymptotic expansions for contour integrals with coalescing saddle points, and for solutions of linear second-order ordinary differential equations with a simple turning point. …

3: 33.12 Asymptotic Expansions for Large $\eta$

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§33.12(ii) Uniform Expansions

… ►The first set is in terms of Airy functions and the expansions are uniform for fixed $\mathrm{\ell }$ and , where $\delta$ is an arbitrary small positive constant. … ►

4: 10.69 Uniform Asymptotic Expansions for Large Order

§10.69 Uniform Asymptotic Expansions for Large Order

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5: 10.57 Uniform Asymptotic Expansions for Large Order

§10.57 Uniform Asymptotic Expansions for Large Order

►Asymptotic expansions for ${𝗃}_n\left((n+\frac{1}{2})z\right)$, ${𝗒}_n\left((n+\frac{1}{2})z\right)$, ${𝗁}_n^{(1)}\left((n+\frac{1}{2})z\right)$, ${𝗁}_n^{(2)}\left((n+\frac{1}{2})z\right)$, ${𝗂}_n^{(1)}\left((n+\frac{1}{2})z\right)$, and ${𝗄}_n\left((n+\frac{1}{2})z\right)$ as $n\to \mathrm{\infty }$ that are uniform with respect to $z$ can be obtained from the results given in §§10.20 and 10.41 by use of the definitions (10.47.3)–(10.47.7) and (10.47.9). …

6: 8.25 Methods of Computation

… ►DiDonato and Morris (1986) describes an algorithm for computing $P(a,x)$ and $Q(a,x)$ for $a\ge 0$, $x\ge 0$, and $a+x\ne 0$ from the uniform expansions in §8.12. …

7: Bibliography Q

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Uniform asymptotic expansions of a double integral: Coalescence of two stationary points. Proc. Roy. Soc. London Ser. A 456, pp. 407–431.

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External Links:

ISSN 1364-5021, Document, MathReview (F. Ursell), ZentralBlatt

Referenced by:

§2.4(vi).

Encodings:

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8: 8.12 Uniform Asymptotic Expansions for Large Parameter

§8.12 Uniform Asymptotic Expansions for Large Parameter

… ►A different type of uniform expansion with coefficients that do not possess a removable singularity at $z=a$ is given by … ►

Inverse Function

… ►These expansions involve the inverse error function $\mathrm{inverfc}\left(x\right)$ (§7.17), and are uniform with respect to $q\in [0,1]$. …

9: 14.32 Methods of Computation

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Application of the uniform asymptotic expansions for large values of the parameters given in §§14.15 and 14.20(vii)–14.20(ix).

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10: 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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External Links:

ISSN 1073-2772, Pdf, MathReview (Éric Delabaere), ZentralBlatt

Referenced by:

§8.12.

Encodings:

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Uniform asymptotic expansions for hypergeometric functions with large parameters. I. Analysis and Applications (Singapore) 1 (1), pp. 111–120.

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External Links:

ISSN 0219-5305, Document, MathReview, ZentralBlatt

Referenced by:

§15.12(iii).

Encodings:

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Uniform asymptotic expansions for hypergeometric functions with large parameters. II. Analysis and Applications (Singapore) 1 (1), pp. 121–128.

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External Links:

ISSN 0219-5305, Document, MathReview, ZentralBlatt

Referenced by:

§15.12(iii).

Encodings:

BibTeX

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Uniform asymptotic expansions for hypergeometric functions with large parameters. III. Analysis and Applications (Singapore) 8 (2), pp. 199–210.

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External Links:

ISSN 0219-5305, Document, MathReview (Javier Segura), ZentralBlatt

Referenced by:

§15.12(iii).

Encodings:

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Scattering by a parabolic cylinder—a uniform asymptotic expansion. J. Math. Phys. 26 (4), pp. 854–860.

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External Links:

ISSN 0022-2488, Document, MathReview (Jean-Louis Guiraud)

Referenced by:

§12.17.

Encodings:

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