asymptotic estimate

SearchAdvancedHelp

(0.001 seconds)

31—33 of 33 matching pages

31: Bibliography H

… ►

Asymptotic expansion of Laplace transforms near the origin. SIAM J. Math. Anal. 1 (1), pp. 118–130.

ⓘ

External Links:

Document, MathReview (E. Riekstiņš), ZentralBlatt

Referenced by:

§2.5(iii), §2.5(ii).

Encodings:

BibTeX

►

Asymptotic expansion of a class of integral transforms with algebraically dominated kernels. J. Math. Anal. Appl. 35 (2), pp. 405–433.

ⓘ

External Links:

Document, MathReview (E. L. Koh), ZentralBlatt

Referenced by:

§2.5(ii).

Encodings:

BibTeX

… ►

Asymptotic formulae in combinatory analysis. Proc. London Math. Soc. (2) 17, pp. 75–115.

ⓘ

Notes:

Reprinted in Ramanujan (1962, pp. 276–309).

External Links:

Document, MathReview Entry, ZentralBlatt

Referenced by:

§27.14(iii).

Encodings:

BibTeX

… ►

Applied and Computational Complex Analysis. Vol. 2: Special Functions—Integral Transforms—Asymptotics—Continued Fractions. Wiley-Interscience [John Wiley & Sons], New York.

ⓘ

Notes:

Reprinted in 1991.

External Links:

ISBN 0-471-01525-3, MathReview (A. E. Heins), ZentralBlatt

Referenced by:

§1.11(v), Ch.3.

Encodings:

BibTeX

… ►

Estimates of the stability intervals for Hill’s equation. Proc. Amer. Math. Soc. 14 (6), pp. 930–932.

ⓘ

External Links:

FullText, MathReview (P. Ungar), ZentralBlatt

Referenced by:

§28.29(iii).

Encodings:

BibTeX

…

32: 30.16 Methods of Computation

… ►If $|{\gamma }^2|$ is large we can use the asymptotic expansions in §30.9. … ►If $|{\gamma }^2|$ is large, then we can use the asymptotic expansions referred to in §30.9 to approximate ${\mathrm{𝖯𝗌}}_n^m(x,{\gamma }^2)$. … ►For error estimates see Volkmer (2004a). …

33: 13.2 Definitions and Basic Properties

… ►

13.2.6 $$U(a,b,z)\sim z^{-a},$$ $z\to \mathrm{\infty }$, $|\mathrm{ph}z|\le \frac{3}{2}\pi -\delta$,

ⓘ

Defines:

$U(a,b,z)$: Kummer confluent hypergeometric function

Symbols:

$\sim$: asymptotic equality, $\pi$: the ratio of the circumference of a circle to its diameter, $\mathrm{ph}$: phase, $z$: complex variable and $\delta$: small positive constant

Referenced by:

§13.2(i), §13.2(iv)

Permalink:

http://dlmf.nist.gov/13.2.E6

Encodings:

pMML, png, TeX

See also:

Annotations for §13.2(i), §13.2(i), §13.2 and Ch.13

… ►

13.2.16 $$U(a,b,z)=\frac{\mathrm{\Gamma }\left(b-1\right)}{\mathrm{\Gamma }\left(a\right)}{z}^{1-b}+O\left(z^{2-\mathrm{\Re }b}\right),$$ $\mathrm{\Re }b\ge 2$, $b\ne 2$,

ⓘ

Symbols:

$O\left(x\right)$: order not exceeding, $\mathrm{\Gamma }\left(z\right)$: gamma function, $U(a,b,z)$: Kummer confluent hypergeometric function, $\mathrm{\Re }$: real part and $z$: complex variable

A&S Ref:

13.5.6 (with order estimate corrected)

Permalink:

http://dlmf.nist.gov/13.2.E16

Encodings:

pMML, png, TeX

See also:

Annotations for §13.2(iii), §13.2 and Ch.13

… ►

13.2.23 $$𝐌(a,b,z)\sim {\mathrm{e}}^z{z}^{a-b}/\mathrm{\Gamma }\left(a\right),$$ $\left|\mathrm{ph}z\right|\le \frac{1}{2}\pi -\delta$,

ⓘ

Symbols:

$\mathrm{\Gamma }\left(z\right)$: gamma function, $𝐌(a,b,z)$: Olver’s confluent hypergeometric function, $\sim$: asymptotic equality, $\pi$: the ratio of the circumference of a circle to its diameter, $\mathrm{e}$: base of natural logarithm, $\mathrm{ph}$: phase, $z$: complex variable and $\delta$: small positive constant

Permalink:

http://dlmf.nist.gov/13.2.E23

Encodings:

pMML, png, TeX

See also:

Annotations for §13.2(iv), §13.2 and Ch.13

…