representation via plane algebraic curve

SearchAdvancedHelp

(0.002 seconds)

11—20 of 378 matching pages

11: Bibliography B

… ►

Integral representations and summations of the modified Struve function. Acta Math. Hungar. 141 (3), pp. 254–281.

ⓘ

External Links:

ISSN 0236-5294, Document, FullText, MathReview (Eugenia N. Petropoulou), ZentralBlatt

Referenced by:

§11.7(v), §11.7(v).

Encodings:

BibTeX

… ►

A new asymptotic representation for $\zeta (\frac{1}{2}+it)$ and quantum spectral determinants. Proc. Roy. Soc. London Ser. A 437, pp. 151–173.

ⓘ

External Links:

ISSN 0962-8444, MathReview (Jack Quine), ZentralBlatt

Referenced by:

§25.9.

Encodings:

BibTeX

… ►

From Klein to Painlevé via Fourier, Laplace and Jimbo. Proc. London Math. Soc. (3) 90 (1), pp. 167–208.

ⓘ

External Links:

ISSN 0024-6115, Document, MathReview (Andrei A. Kapaev), ZentralBlatt

Referenced by:

§32.9(iii).

Encodings:

BibTeX

… ►

Plane Algebraic Curves. Birkhäuser Verlag, Basel.

ⓘ

Notes:

Translated from the German by John Stillwell

External Links:

ISBN 3-7643-1769-8, MathReview, ZentralBlatt

Referenced by:

§21.7(i).

Encodings:

BibTeX

… ►

Riemann zeta function: Rapidly converging series and integral representations. Appl. Math. Lett. 5 (2), pp. 83–88.

ⓘ

External Links:

ISSN 0893-9659, Document, MathReview (Jacek Fabrykowski), ZentralBlatt

Referenced by:

§25.18(i).

Encodings:

BibTeX

…

12: Bibliography S

… ►

The Symmetric Group: Representations, Combinatorial Algorithms, and Symmetric Functions. 2nd edition, Graduate Texts in Mathematics, Vol. 203, Springer-Verlag, New York.

ⓘ

Notes:

First edition published by Wadsworth & Brooks/Cole Advanced Books & Software, 1991.

External Links:

ISBN 0-387-95067-2, MathReview, ZentralBlatt

Referenced by:

§26.19.

Encodings:

BibTeX

… ►

Time propagation of partial differential equations using the short iterative Lanczos method and finite-element discrete variable representation. Adv. Quantum Chem. 72, pp. 95–127.

ⓘ

Referenced by:

§18.38(i).

Encodings:

BibTeX

… ►

On integral representations for Lamé and other special functions. SIAM J. Math. Anal. 11 (4), pp. 702–723.

ⓘ

External Links:

ISSN 0036-1410, Document, MathReview (R. K. Gupta), ZentralBlatt

Referenced by:

§29.17(i), §29.8.

Encodings:

BibTeX

… ►

On integral representation of Weber’s parabolic cylinder function and its expansion into an infinite series. J. Indian Math. Soc. (N. S.) 4, pp. 34–38.

ⓘ

External Links:

MathReview (M. C. Gray), ZentralBlatt

Referenced by:

§12.13(ii).

Encodings:

BibTeX

… ►

Représentation asymptotique des fonctions de Mathieu et des fonctions d’onde sphéroidales. Trans. Amer. Math. Soc. 66 (1), pp. 93–134 (French).

ⓘ

External Links:

FullText, MathReview (M. Strutt), ZentralBlatt

Referenced by:

§28.8(ii).

Encodings:

BibTeX

…

13: 19.30 Lengths of Plane Curves

§19.30 Lengths of Plane Curves

►

§19.30(i) Ellipse

… ►

§19.30(ii) Hyperbola

… ►For other plane curves with arclength representable by an elliptic integral see Greenhill (1892, p. 190) and Bowman (1953, pp. 32–33).

14: 21.7 Riemann Surfaces

… ►

§21.7(i) Connection of Riemann Theta Functions to Riemann Surfaces

… ►Belokolos et al. (1994, §2.1)), they are obtainable from plane algebraic curves (Springer (1957), or Riemann (1851)). …Equation (21.7.1) determines a plane algebraic curve in ${ℂ}^2$, which is made compact by adding its points at infinity. … ►If a local coordinate $z$ is chosen on the Riemann surface, then the local coordinate representation of these holomorphic differentials is given by … ►These are Riemann surfaces that may be obtained from algebraic curves of the form …

15: 15.17 Mathematical Applications

… ►The quotient of two solutions of (15.10.1) maps the closed upper half-plane $\mathrm{\Im }z\ge 0$ conformally onto a curvilinear triangle. … ►

§15.17(iii) Group Representations

… ►These monodromy groups are finite iff the solutions of Riemann’s differential equation are all algebraic. …

16: 4.13 Lambert $W$-Function

… ►

►►

Figure 4.13.2: The $W\left(z\right)$ function on the first 5 Riemann sheets. $W\left(z\right)$ maps the first Riemann sheet in the middle of the left-hand side to the region enclosed by the green curve on the right-hand side; it maps the Riemann sheet on the left-hand side to the region enclosed by the pink, green and orange curves on the right-hand side, etc. Magnify

… ►Explicit representations for the $p_n(x)$ are given in Kalugin and Jeffrey (2011). … ►

4.13.5_1 $${\left(\frac{W_0\left(z\right)}{z}\right)}^a={\mathrm{e}}^{-a{W}_0\left(z\right)}=\sum _{n=0}^{\mathrm{\infty }}\frac{a{\left(n+a\right)}^{n-1}}{n!}{\left(-z\right)}^n,$$ , $a\in ℂ$.

ⓘ

Symbols:

$W\left(z\right)$: Lambert $W$-function, $ℂ$: complex plane, $\in$: element of, $\mathrm{e}$: base of natural logarithm, $!$: factorial (as in $n!$), $n$: integer, $a$: real or complex constant and $z$: complex variable

Notes:

See Corless et al. (1996, formula (2.36)).

Referenced by:

§4.13, Erratum (V1.1.7) for Expansion

Permalink:

http://dlmf.nist.gov/4.13.E5_1

Encodings:

pMML, png, TeX

Addition (effective with 1.1.7):

This equation was added.

See also:

Annotations for §4.13 and Ch.4

… ►See Jeffrey and Murdoch (2017) for an explicit representation for the $c_n$ in terms of associated Stirling numbers. … ►For these and other integral representations of the Lambert $W$-function see Kheyfits (2004), Kalugin et al. (2012) and Mező (2020). …

17: 14.26 Uniform Asymptotic Expansions

… ►The uniform asymptotic approximations given in §14.15 for $P_{\nu }^{-\mu }\left(x\right)$ and ${𝑸}_{\nu }^{\mu }\left(x\right)$ for are extended to domains in the complex plane in the following references: §§14.15(i) and 14.15(ii), Dunster (2003b); §14.15(iii), Olver (1997b, Chapter 12); §14.15(iv), Boyd and Dunster (1986). … ►See also Frenzen (1990), Gil et al. (2000), Shivakumar and Wong (1988), Ursell (1984), and Wong (1989) for uniform asymptotic approximations obtained from integral representations.

18: 25.11 Hurwitz Zeta Function

… ►

§25.11(iii) Representations by the Euler–Maclaurin Formula

… ►

§25.11(iv) Series Representations

… ►

§25.11(vii) Integral Representations

… ►

§25.11(viii) Further Integral Representations

… ►

§25.11(x) Further Series Representations

…

19: 16.17 Definition

… ►Then the Meijer $G$-function is defined via the Mellin–Barnes integral representation: … ►

…

Figure 16.17.1: s-plane. Path $L$ for the integral representation (16.17.1) of the Meijer $G$-function.

…

20: Bibliography K

… ►

Series expansions for the third incomplete elliptic integral via partial fraction decompositions. J. Comput. Appl. Math. 207 (2), pp. 331–337.

ⓘ

External Links:

ISSN 0377-0427, Document, MathReview (José Luis López), ZentralBlatt

Referenced by:

§19.12, §19.5.

Encodings:

BibTeX

… ►

Closed-form representations of the Lambert $W$ function. Fract. Calc. Appl. Anal. 7 (2), pp. 177–190.

ⓘ

External Links:

ISSN 1311-0454, MathReview (Lewis H. Ryder), ZentralBlatt

Referenced by:

§4.13.

Encodings:

BibTeX

… ►

Algebraic Aspects of Cryptography. Springer-Verlag, Berlin.

ⓘ

Notes:

Second printing with corrections

External Links:

ISBN 3-540-63446-0, MathReview (M. V. D. Burmester), ZentralBlatt

Referenced by:

§23.20(iii).

Encodings:

BibTeX

… ►

Meixner-Pollaczek polynomials and the Heisenberg algebra. J. Math. Phys. 30 (4), pp. 767–769.

ⓘ

External Links:

ISSN 0022-2488, Document, MathReview, ZentralBlatt

Referenced by:

§18.21(ii).

Encodings:

BibTeX

… ►

Compact quantum groups and $q$-special functions. In Representations of Lie Groups and Quantum Groups, Pitman Res. Notes Math. Ser., Vol. 311, pp. 46–128.

ⓘ

Notes:

Sections 3 and 4 also available as arXiv:math/9403216

External Links:

MathReview (Eric M. Opdam)

Referenced by:

(18.27.14_3).

Encodings:

BibTeX

…