large %CE%BA

SearchAdvancedHelp

(0.001 seconds)

21—30 of 165 matching pages

21: 33.21 Asymptotic Approximations for Large $|r|$

§33.21 Asymptotic Approximations for Large $|r|$

►

§33.21(i) Limiting Forms

… ►

§33.21(ii) Asymptotic Expansions

…

22: 8.20 Asymptotic Expansions of $E_p\left(z\right)$

… ►

§8.20(i) Large $z$

… ►

§8.20(ii) Large $p$

…

23: Bibliography N

… ►

The resurgence properties of the large order asymptotics of the Anger-Weber function I. J. Class. Anal. 4 (1), pp. 1–39.

ⓘ

External Links:

ISSN 1848-5979, Document, Link, MathReview (José Luis López), ZentralBlatt

Referenced by:

(11.11.10), (11.11.8), §11.11(iii).

Encodings:

BibTeX

►

The resurgence properties of the large order asymptotics of the Anger-Weber function II. J. Class. Anal. 4 (2), pp. 121–147.

ⓘ

External Links:

ISSN 1848-5979, Document, Link, MathReview Entry, ZentralBlatt

Referenced by:

(11.11.10), (11.11.8), §11.11(iii).

Encodings:

BibTeX

… ►

On the large argument asymptotics of the Lommel function via Stieltjes transforms. Asymptot. Anal. 91 (3-4), pp. 265–281.

ⓘ

External Links:

ISSN 0921-7134, Document, MathReview Entry, ZentralBlatt

Referenced by:

§11.6(iii), §11.6(iii), §11.9(iii), §11.9(iii).

Encodings:

BibTeX

… ►

Error Bounds for the Large-Argument Asymptotic Expansions of the Hankel and Bessel Functions. Acta Appl. Math. 150, pp. 141–177.

ⓘ

External Links:

ISSN 0167-8019, Document, MathReview Entry, ZentralBlatt

Referenced by:

(9.7.16), (9.7.17), §9.7(iii), §9.7(iv).

Encodings:

BibTeX

►

Error bounds for the large-argument asymptotic expansions of the Lommel and allied functions. Stud. Appl. Math. 140 (4), pp. 508–541.

ⓘ

External Links:

ISSN 0022-2526, Document, Link, MathReview (Pedro J. Pagola), ZentralBlatt

Referenced by:

§11.11(i), §11.11(i).

Encodings:

BibTeX

…

24: 10.40 Asymptotic Expansions for Large Argument

§10.40 Asymptotic Expansions for Large Argument

… ►

Products

… ► ►

$\nu$-Derivative

… ►

§10.40(iv) Exponentially-Improved Expansions

…

25: 11.13 Methods of Computation

… ►Although the power-series expansions (11.2.1) and (11.2.2), and the Bessel-function expansions of §11.4(iv) converge for all finite values of $z$, they are cumbersome to use when $|z|$ is large owing to slowness of convergence and cancellation. For large $|z|$ and/or $|\nu |$ the asymptotic expansions given in §11.6 should be used instead. … ►Then from the limiting forms for small argument (§§11.2(i), 10.7(i), 10.30(i)), limiting forms for large argument (§§11.6(i), 10.7(ii), 10.30(ii)), and the connection formulas (11.2.5) and (11.2.6), it is seen that ${𝐇}_{\nu }\left(x\right)$ and ${𝐋}_{\nu }\left(x\right)$ can be computed in a stable manner by integrating forwards, that is, from the origin toward infinity. The solution ${𝐊}_{\nu }\left(x\right)$ needs to be integrated backwards for small $x$, and either forwards or backwards for large $x$ depending whether or not $\nu$ exceeds $\frac{1}{2}$. …

26: 28.34 Methods of Computation

… ►

Use of asymptotic expansions and approximations for large $q$ (§§28.8(i), 28.16). See also Zhang and Jin (1996, pp. 482–485).

… ►

Use of asymptotic expansions and approximations for large $q$ (§§28.8(ii)–28.8(iv)).

… ►

Use of asymptotic expansions for large $z$ or large $q$. See §§28.25 and 28.26.

27: 29.16 Asymptotic Expansions

… ►The approximations for Lamé polynomials hold uniformly on the rectangle $0\le \mathrm{\Re }z\le K$, $0\le \mathrm{\Im }z\le K^{\prime }$, when $nk$ and $n{k}^{\prime }$ assume large real values. …

28: 33.10 Limiting Forms for Large $\rho$ or Large $\left|\eta \right|$

§33.10 Limiting Forms for Large $\rho$ or Large $\left|\eta \right|$

►

§33.10(i) Large $\rho$

… ►

§33.10(ii) Large Positive $\eta$

… ►

§33.10(iii) Large Negative $\eta$

…

29: Ronald F. Boisvert

… ►He is also Editor at Large for the DLMF Project. …

30: 28.26 Asymptotic Approximations for Large $q$

§28.26 Asymptotic Approximations for Large $q$

… ►

§28.26(ii) Uniform Approximations

…