elliptic crack and punch problems

SearchAdvancedHelp

(0.002 seconds)

11—20 of 37 matching pages

11: Bibliography H

… ►

Solving Ordinary Differential Equations. I. Nonstiff Problems. 2nd edition, Springer Series in Computational Mathematics, Vol. 8, Springer-Verlag, Berlin.

ⓘ

Notes:

A reprinting with corrections appeared in 2000.

External Links:

ISBN 3-540-56670-8, MathReview, ZentralBlatt

Referenced by:

§3.7(v), §3.7(i).

Encodings:

BibTeX

►

Solving Ordinary Differential Equations. I. Nonstiff Problems. 2nd edition, Springer-Verlag, Berlin.

ⓘ

External Links:

ISBN 3-540-56670-8, Document, MathReview

Referenced by:

§32.17.

Encodings:

BibTeX

►

Solving Ordinary Differential Equations. II. Stiff and Differential-Algebraic Problems. 2nd edition, Springer Series in Computational Mathematics, Vol. 14, Springer-Verlag, Berlin.

ⓘ

External Links:

ISBN 3-540-60452-9, MathReview, ZentralBlatt

Referenced by:

§3.7(v).

Encodings:

BibTeX

… ►

Some problems of “Partitio Numerorum” (VI): Further researches in Waring’s Problem. Math. Z. 23, pp. 1–37.

ⓘ

Notes:

Reprinted in Collected Papers of G. H. Hardy (Including Joint papers with J. E. Littlewood and others), Vol. I, pp. 469–505, Clarendon Press, Oxford, 1966.

External Links:

ISSN 0025-5874, Document, MathReview Entry, ZentralBlatt

Referenced by:

§27.13(iii).

Encodings:

BibTeX

… ►

A boundary value problem associated with the second Painlevé transcendent and the Korteweg-de Vries equation. Arch. Rational Mech. Anal. 73 (1), pp. 31–51.

ⓘ

External Links:

ISSN 0003-9527, Document, MathReview (Richard Brown), ZentralBlatt

Referenced by:

§32.11(ii).

Encodings:

BibTeX

…

12: 19.34 Mutual Inductance of Coaxial Circles

… ►References for other inductance problems solvable in terms of elliptic integrals are given in Grover (1946, pp. 8 and 283).

13: 23.20 Mathematical Applications

… ►For applications of the Weierstrass function and the elliptic curve method to these problems see Bressoud (1989) and Koblitz (1999). …

14: Bibliography B

… ►

Coefficient functions for an inhomogeneous turning-point problem. Mathematika 38 (2), pp. 217–238.

ⓘ

External Links:

ISSN 0025-5793, MathReview (Archibald D. MacGillivray), ZentralBlatt

Referenced by:

§2.8(iii).

Encodings:

BibTeX

… ►

Some solutions of the problem of forced convection. Philos. Mag. Series 7 20, pp. 322–343.

ⓘ

External Links:

Document, ZentralBlatt

Referenced by:

§10.73(iv).

Encodings:

BibTeX

… ►

Numerical Methods for Least Squares Problems. Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA.

ⓘ

External Links:

ISBN 0-89871-360-9, MathReview (Hongyuan Zha), ZentralBlatt

Referenced by:

§3.11(v).

Encodings:

BibTeX

… ►

Semiclassical asymptotics of orthogonal polynomials, Riemann-Hilbert problem, and universality in the matrix model. Ann. of Math. (2) 150 (1), pp. 185–266.

ⓘ

External Links:

ISSN 0003-486X, Document, MathReview (Thomas Kriecherbauer), ZentralBlatt

Referenced by:

§18.32.

Encodings:

BibTeX

… ►

Problem of two Coulomb centres at large intercentre separation: Asymptotic expansions from analytical solutions of the Heun equation. J. Phys. A 30 (2), pp. 559–571.

ⓘ

External Links:

ISSN 0305-4470, Document, MathReview, ZentralBlatt

Referenced by:

§31.13.

Encodings:

BibTeX

…

15: 29.15 Fourier Series and Chebyshev Series

… ►Equations (29.6.4), with $p=1,2,\mathrm{\dots },n$, (29.6.3), and $A_{2n+2}=0$ can be cast as an algebraic eigenvalue problem in the following way. … ►Since (29.2.5) implies that $\cos \varphi =\mathrm{sn}(z,k)$, (29.15.1) can be rewritten in the form …This determines the polynomial $P$ of degree $n$ for which ${\mathrm{𝑢𝐸}}_{2n}^m(z,k^2)=P({\mathrm{sn}}^2(z,k))$; compare Table 29.12.1. … ►

29.15.49 $${\mathrm{𝑐𝑑𝐸}}_{2n+2}^m(z,k^2)=\mathrm{cn}(z,k)\mathrm{dn}(z,k)\sum _{p=0}^n{D}_{2p+1}{U}_{2p}\left(\mathrm{sn}(z,k)\right),$$

ⓘ

Symbols:

$U_n\left(x\right)$: Chebyshev polynomial of the second kind, $\mathrm{cn}(z,k)$: Jacobian elliptic function, $\mathrm{dn}(z,k)$: Jacobian elliptic function, $\mathrm{sn}(z,k)$: Jacobian elliptic function, ${\mathrm{𝑐𝑑𝐸}}_{2n+2}^m(z,k^2)$: Lamé polynomial, $m$: nonnegative integer, $n$: nonnegative integer, $p$: nonnegative integer, $z$: complex variable, $k$: real parameter and $D_{2p}$: coefficents

Permalink:

http://dlmf.nist.gov/29.15.E49

Encodings:

pMML, png, TeX

See also:

Annotations for §29.15(ii), §29.15 and Ch.29

►

29.15.50 $${\mathrm{𝑠𝑐𝑑𝐸}}_{2n+3}^m(z,k^2)=\mathrm{cn}(z,k)\mathrm{dn}(z,k)\sum _{p=0}^n{D}_{2p+2}{U}_{2p+1}\left(\mathrm{sn}(z,k)\right).$$

ⓘ

Symbols:

$U_n\left(x\right)$: Chebyshev polynomial of the second kind, $\mathrm{cn}(z,k)$: Jacobian elliptic function, $\mathrm{dn}(z,k)$: Jacobian elliptic function, $\mathrm{sn}(z,k)$: Jacobian elliptic function, ${\mathrm{𝑠𝑐𝑑𝐸}}_{2n+3}^m(z,k^2)$: Lamé polynomial, $m$: nonnegative integer, $n$: nonnegative integer, $p$: nonnegative integer, $z$: complex variable, $k$: real parameter and $D_{2p+1}$: coefficents

Permalink:

http://dlmf.nist.gov/29.15.E50

Encodings:

pMML, png, TeX

See also:

Annotations for §29.15(ii), §29.15 and Ch.29

…

16: Bibliography

… ►

Rational and elliptic solutions of the Korteweg-de Vries equation and a related many-body problem. Comm. Pure Appl. Math. 30 (1), pp. 95–148.

ⓘ

External Links:

MathReview (Alexander A. Pankov), ZentralBlatt

Referenced by:

§23.21(ii).

Encodings:

BibTeX

…

17: Bibliography L

… ►

The two-point connection problem for differential equations of the Heun class. Teoret. Mat. Fiz. 101 (3), pp. 360–368 (Russian).

ⓘ

Notes:

In Russian. English translation: Theoret. and Math. Phys. 101(1994), no. 3, pp. 1413–1418 (1995)

External Links:

ISSN 0564-6162, Document, MathReview, ZentralBlatt

Referenced by:

§31.18.

Encodings:

BibTeX

… ►

The central two-point connection problem for the Heun class of ODEs. J. Phys. A 31 (18), pp. 4249–4261.

ⓘ

External Links:

ISSN 0305-4470, Document, MathReview, ZentralBlatt

Referenced by:

§31.12.

Encodings:

BibTeX

… ►

Solutions to a generalized spheroidal wave equation: Teukolsky’s equations in general relativity, and the two-center problem in molecular quantum mechanics. J. Math. Phys. 27 (5), pp. 1238–1265.

ⓘ

External Links:

ISSN 0022-2488, Document, MathReview (Basilis C. Xanthopoulos), ZentralBlatt

Referenced by:

§30.12, §31.17(ii).

Encodings:

BibTeX

… ►

Problems of Mathematical Physics. Revised, enlarged and corrected English edition; translated and edited by Richard A. Silverman. With a supplement by Edward L. Reiss, Prentice-Hall Inc., Englewood Cliffs, N.J..

ⓘ

Notes:

Republished as Worked Problems in Applied Mathematics by Dover Publications, New York, 1979

External Links:

ISBN 0-486-63730-1, MathReview (J. Mathews), ZentralBlatt

Referenced by:

§10.43(v).

Encodings:

BibTeX

… ►

On incomplete Airy functions and their application to diffraction problems. Radio Sci. 4 (10), pp. 959–969.

ⓘ

External Links:

ISSN 0048-6604, Document, MathReview (T. Erber)

Referenced by:

§9.14.

Encodings:

BibTeX

…

18: Bibliography G

… ►

Quasirandom distributed bases for bound problems. J. Chem. Phys. 114 (9), pp. 3929–3939.

ⓘ

Referenced by:

§18.39(iii).

Encodings:

BibTeX

►

The solution of Cauchy’s problem for two totally hyperbolic linear differential equations by means of Riesz integrals. Ann. of Math. (2) 48 (4), pp. 785–826.

ⓘ

External Links:

FullText, MathReview (E. T. Copson), ZentralBlatt

Referenced by:

§35.2, §35.3(ii).

Encodings:

BibTeX

… ►

Problem 72-21, Laplace transforms of Airy functions. SIAM Rev. 15 (4), pp. 796–798.

ⓘ

Notes:

Problem proposed by P. Smith.

External Links:

Document

Referenced by:

(9.10.14), (9.10.15), (9.10.16), §9.10(v).

Encodings:

BibTeX

… ►

An extended class of orthogonal polynomials defined by a Sturm-Liouville problem. J. Math. Anal. Appl. 359 (1), pp. 352–367.

ⓘ

External Links:

ISSN 0022-247X, Document, Link, MathReview (Li Zhong Peng)

Referenced by:

§18.36(vi).

Encodings:

BibTeX

… ►

Stirling number representation problems. Proc. Amer. Math. Soc. 11 (3), pp. 447–451.

ⓘ

External Links:

FullText, MathReview (L. Carlitz), ZentralBlatt

Referenced by:

§26.1, §26.1, Notations S, Notations S.

Encodings:

BibTeX

…

19: 28.32 Mathematical Applications

… ►If the boundary conditions in a physical problem relate to the perimeter of an ellipse, then elliptical coordinates are convenient. …

20: Bibliography R

… ►

Plane wave scattering by a conducting elliptic cylinder coated by a nonconfocal dielectric. IEEE Trans. Antennas and Propagation 39 (2), pp. 218–223.

ⓘ

External Links:

Document

Referenced by:

6th item.

Encodings:

BibTeX

… ►

Elliptic Functions, Theta Functions, and Riemann Surfaces. The Williams & Wilkins Co., Baltimore, MD.

ⓘ

External Links:

MathReview (H. H. Martens), ZentralBlatt

Referenced by:

§20.11(iv), §20.12(ii).

Encodings:

BibTeX

… ►

General Computation Methods of Chebyshev Approximation. The Problems with Linear Real Parameters. Publishing House of the Academy of Science of the Ukrainian SSR, Kiev.

ⓘ

Notes:

English translation, AEC-TR-4491, United States Atomic Energy Commission

External Links:

MathReview (A. S. Householder)

Referenced by:

§3.11(iii).

Encodings:

BibTeX

… ►

Elliptic hypergeometric series on root systems. Adv. Math. 181 (2), pp. 417–447.

ⓘ

External Links:

ISSN 0001-8708, Document, MathReview, ZentralBlatt

Referenced by:

§20.11(iii).

Encodings:

BibTeX

… ►

The problem of an infinite plate under an inclined loading, with tables of the integrals of $\mathrm{Ai}(\pm \mathrm{x})$ and $\mathrm{Bi}(\pm \mathrm{x})$ . Quart. J. Mech. Appl. Math. 7 (1), pp. 1–7.

ⓘ

External Links:

Document, MathReview (A. Erdélyi), ZentralBlatt

Referenced by:

§9.16, 1st item.

Encodings:

BibTeX

…