Lambert%20W-function

SearchAdvancedHelp

(0.005 seconds)

11—20 of 113 matching pages

11: Bibliography S

… ►

Transformations of the Jacobian amplitude function and its calculation via the arithmetic-geometric mean. SIAM J. Math. Anal. 20 (6), pp. 1514–1528.

ⓘ

External Links:

ISSN 0036-1410, Document, MathReview (J. M. H. Peters), ZentralBlatt

Referenced by:

§22.19(i), §22.20(vi).

Encodings:

BibTeX

… ►

Numerics of the generalized Lambert $W$ function. ACM Commun. Comput. Algebra 48 (2), pp. 42–56.

ⓘ

External Links:

FullText, Document, MathReview Entry, ZentralBlatt

Referenced by:

§4.13, §4.13.

Encodings:

BibTeX

►

Asymptotic series of generalized Lambert $W$ function. ACM Commun. Comput. Algebra 47 (3), pp. 75–83.

ⓘ

External Links:

FullText, ZentralBlatt

Referenced by:

§4.13, §4.13.

Encodings:

BibTeX

►

General relativity and quantum mechanics: towards a generalization of the Lambert $W$ function: a generalization of the Lambert $W$ function. Appl. Algebra Engrg. Comm. Comput. 17 (1), pp. 41–47.

ⓘ

External Links:

ISSN 0938-1279, Document, FullText, MathReview (E. Capelas de Oliveira), ZentralBlatt

Referenced by:

§4.13, §4.13.

Encodings:

BibTeX

… ►

Uniform asymptotic forms of modified Mathieu functions. Quart. J. Mech. Appl. Math. 20 (3), pp. 365–380.

ⓘ

External Links:

Document, MathReview (F. W. J. Olver), ZentralBlatt

Referenced by:

§28.8(iv).

Encodings:

BibTeX

…

12: Bibliography C

… ►

Numerical evaluation of the Lambert $W$ function and application to generation of generalized Gaussian noise with exponent 1/2. IEEE Trans. Signal Process. 50 (9), pp. 2160–2165.

ⓘ

External Links:

ISSN 1053-587X, Document, MathReview (J. Borwein), ZentralBlatt

Referenced by:

§4.44, §4.45(iii).

Encodings:

BibTeX

… ►

Asymptotic estimates for generalized Stirling numbers. Analysis (Munich) 20 (1), pp. 1–13.

ⓘ

External Links:

ISSN 0174-4747, MathReview (F. T. Howard), ZentralBlatt

Referenced by:

§26.8(vii).

Encodings:

BibTeX

… ►

Validated computation of certain hypergeometric functions. ACM Trans. Math. Software 38 (2), pp. Art. 11, 20.

ⓘ

External Links:

ISSN 0098-3500, Document, FullText, MathReview Entry, ZentralBlatt

Referenced by:

§13.29(v), §15.19(v).

Encodings:

BibTeX

… ►

On the Lambert $W$ function. Adv. Comput. Math. 5 (4), pp. 329–359.

ⓘ

External Links:

ISSN 1019-7168, MathReview, ZentralBlatt

Referenced by:

(4.13.10), (4.13.11), (4.13.1_1), (4.13.5_1), §4.13, §4.44, §4.44.

Encodings:

BibTeX

… ►

A sequence of series for the Lambert $W$ function. In Proceedings of the 1997 International Symposium on Symbolic and Algebraic Computation (Kihei, HI), pp. 197–204.

ⓘ

External Links:

Document, Link, MathReview Entry, ZentralBlatt

Referenced by:

(4.13.4_1), (4.13.4_2), (4.13.5_2), §4.13.

Encodings:

BibTeX

…

13: Software Index

… ► ►►►►

	Open Source													With Book						Commercial
…
4.48(iv) Lambert $W$-Function	✓					✓			✓			✓	✓								✓	✓	a
…
20 Theta Functions
…

…

14: 25.18 Methods of Computation

… ►For dilogarithms and polylogarithms see Jacobs and Lambert (1972), Osácar et al. (1995), Spanier and Oldham (1987, pp. 231–232), and Zudilin (2007). …

15: Errata

… ►

§4.13 has been enlarged. The Lambert $W$-function is multi-valued and we use the notation $W_k\left(x\right)$, $k\in \mathbb{Z}$, for the branches. The original two solutions are identified via $\mathrm{Wp}\left(x\right)=W_0\left(x\right)$ and $\mathrm{Wm}\left(x\right)=W_{\pm 1}\left(x\mp 0\mathrm{i}\right)$.

Other changes are the introduction of the Wright $\omega$-function and tree $T$-function in (4.13.1_2) and (4.13.1_3), simplification formulas (4.13.3_1) and (4.13.3_2), explicit representation (4.13.4_1) for $\frac{d^{n}W}{{dz}^n}$, additional Maclaurin series (4.13.5_1) and (4.13.5_2), an explicit expansion about the branch point at $z=-{\mathrm{e}}^{-1}$ in (4.13.9_1), extending the number of terms in asymptotic expansions (4.13.10) and (4.13.11), and including several integrals and integral representations for Lambert $W$-functions in the end of the section.

… ►

4.13.11 $$\mathrm{Wm}\left(x\right)=-\eta -\ln \eta -\frac{\ln \eta }{\eta }+\frac{{(\ln \eta )}^2}{2{\eta }^2}-\frac{\ln \eta }{{\eta }^2}+O\left(\frac{{(\ln \eta )}^3}{{\eta }^3}\right)$$

Originally the sign in front of $\frac{{(\ln \eta )}^2}{2{\eta }^2}$ was $-$. The correct sign is $+$.

… ►

In the final line of this subsection, $\mathrm{Wm}\left(n\right)$ was replaced by $\mathrm{Wp}\left(n\right)$ twice, and the wording was changed from “or, equivalently, $N={\mathrm{e}}^{\mathrm{Wm}\left(n\right)}$” to “or, specifically, $N={\mathrm{e}}^{\mathrm{Wp}\left(n\right)}$”.

Reported by Gergő Nemes on 2018-04-09

… ►

Several new equations have been added. See (8.17.24), (20.7.34), §20.11(v), (26.12.27), (36.2.28), and (36.2.29).

… ►

Bibliographic citations were added in §§1.13(v), 10.14, 10.21(ii), 18.15(v), 18.32, 30.16(iii), 32.13(ii), and as general references in Chapters 19, 20, 22, and 23.

…

16: Bibliography M

… ►

Rational approximations, software and test methods for sine and cosine integrals. Numer. Algorithms 12 (3-4), pp. 259–272.

ⓘ

Notes:

Includes Fortran code, maximum accuracy 20S.

External Links:

ISSN 1017-1398, Document, MathReview, ZentralBlatt

Referenced by:

§6.13, 4th item, §6.21(ii).

Encodings:

BibTeX

… ►

Calculation of the modified Bessel functions of the second kind with complex argument. Math. Comp. 20 (95), pp. 407–412.

ⓘ

External Links:

ISSN 0025-5718, FullText, MathReview (H. E. Fettis), ZentralBlatt

Referenced by:

§10.74(iii).

Encodings:

BibTeX

… ►

Hierarchies and logarithmic oscillations in the temporal relaxation patterns of proteins and other complex systems. Proc. Nat. Acad. Sci. U .S. A. 96 (20), pp. 11085–11089.

ⓘ

External Links:

FullText

Referenced by:

§8.24(i).

Encodings:

BibTeX

►

An integral representation for the Lambert $W$ function.

ⓘ

External Links:

2012.02480

Referenced by:

(4.13.16), §4.13.

Encodings:

BibTeX

… ►

The $q$-analogue of the Laguerre polynomials. J. Math. Anal. Appl. 81 (1), pp. 20–47.

ⓘ

External Links:

ISSN 0022-247X, Document, MathReview (R. A. Askey), ZentralBlatt

Referenced by:

§18.27(v).

Encodings:

BibTeX

…

17: Bibliography J

… ►

On the numerical calculation of polylogarithms. Nordisk Tidskr. Informationsbehandling (BIT) 12 (4), pp. 581–585.

ⓘ

External Links:

Document, MathReview, ZentralBlatt

Referenced by:

§25.18(i).

Encodings:

BibTeX

… ►

Stirling Numbers, Lambert W and the Gamma Function. In Mathematical Aspects of Computer and Information Sciences, J. Blömer, I. S. Kotsireas, T. Kutsia, and D. E. Simos (Eds.), Cham, pp. 275–279.

ⓘ

External Links:

ISBN 978-3-319-72453-9, ZentralBlatt

Referenced by:

§4.13.

Encodings:

BibTeX

…

18: DLMF Project News

error generating summary

19: 8 Incomplete Gamma and Related
Functions

Chapter 8 Incomplete Gamma and Related Functions

…

20: 28 Mathieu Functions and Hill’s Equation

Chapter 28 Mathieu Functions and Hill’s Equation

…