linear transformation

SearchAdvancedHelp

(0.001 seconds)

11—20 of 38 matching pages

11: 19.2 Definitions

… ►Bulirsch’s integrals are linear combinations of Legendre’s integrals that are chosen to facilitate computational application of Bartky’s transformation (Bartky (1938)). …

12: 15.11 Riemann’s Differential Equation

… ►The importance of (15.10.1) is that any homogeneous linear differential equation of the second order with at most three distinct singularities, all regular, in the extended plane can be transformed into (15.10.1). …

13: 18.38 Mathematical Applications

… ►While the Toda equation is an important model of nonlinear systems, the special functions of mathematical physics are usually regarded as solutions to linear equations. …

14: 31.2 Differential Equations

… ►All other homogeneous linear differential equations of the second order having four regular singularities in the extended complex plane, $ℂ\cup \{\mathrm{\infty }\}$, can be transformed into (31.2.1). …

15: Bibliography Z

… ►

Distribution Theory and Transform Analysis, An Introduction and Generalized Functions with Applications. Dover, New York.

ⓘ

Notes:

Reprint of 1965 McGraw-Hill Publication

External Links:

ISBN 0-486-65479-6, MathReview Entry

Referenced by:

§1.16(ix).

Encodings:

BibTeX

►

Weighted derangements and the linearization coefficients of orthogonal Sheffer polynomials. Proc. London Math. Soc. (3) 65 (1), pp. 1–22.

ⓘ

External Links:

ISSN 0024-6115, Document, Link, MathReview (R. A. Askey), ZentralBlatt

Referenced by:

§18.18(v).

Encodings:

BibTeX

►

Error bounds for asymptotic solutions of second-order linear difference equations. J. Comput. Appl. Math. 71 (2), pp. 191–212.

ⓘ

External Links:

ISSN 0377-0427, Document, MathReview, ZentralBlatt

Referenced by:

§2.9(i), §2.9(ii).

Encodings:

BibTeX

… ►

Generalized Watson Transforms and Applications to Group Representations. Ph.D. Thesis, University of Vermont, Burlington,VT.

ⓘ

Referenced by:

§35.7(ii).

Encodings:

BibTeX

►

A fast Fourier-Bessel transform algorithm. Zh. Vychisl. Mat. i Mat. Fiz. 35 (7), pp. 1128–1133 (Russian).

ⓘ

Notes:

English translation in Comput. Math. Math. Phys. 35(7), pp. 901–905

External Links:

ISSN 0044-4669, MathReview (Vítĕzslav Veselý), ZentralBlatt

Referenced by:

§10.74(vii).

Encodings:

BibTeX

…

16: 2.7 Differential Equations

… ►To include the point at infinity in the foregoing classification scheme, we transform it into the origin by replacing $z$ in (2.7.1) with $1/z$; see Olver (1997b, pp. 153–154). For corresponding definitions, together with examples, for linear differential equations of arbitrary order see §§16.8(i)–16.8(ii). … ►See §2.11(v) for other examples. ►The exceptional case $f_0^2=4g_0$ is handled by Fabry’s transformation: …The transformed differential equation either has a regular singularity at $t=\mathrm{\infty }$, or its characteristic equation has unequal roots. …

17: Bibliography W

… ►

Asymptotic expansions for second-order linear difference equations with a turning point. Numer. Math. 94 (1), pp. 147–194.

ⓘ

External Links:

ISSN 0029-599X, Document, MathReview (Sergey M. Zagorodnyuk), ZentralBlatt

Referenced by:

§2.9(iii).

Encodings:

BibTeX

►

Linear difference equations with transition points. Math. Comp. 74 (250), pp. 629–653.

ⓘ

External Links:

ISSN 0025-5718, Document, MathReview (B. G. Pachpatte), ZentralBlatt

Referenced by:

§2.9(iii).

Encodings:

BibTeX

… ►

Linear Turning Point Theory. Applied Mathematical Sciences No. 54, Springer-Verlag, New York.

ⓘ

External Links:

ISBN 0-387-96046-5, MathReview (Anthony Leung), ZentralBlatt

Referenced by:

Ch.9.

Encodings:

BibTeX

… ►

Linear and Nonlinear Waves. John Wiley & Sons, New York.

ⓘ

Notes:

Reprinted in 1999.

External Links:

ISBN 0471359424, MathReview, ZentralBlatt

Referenced by:

§9.16.

Encodings:

BibTeX

… ►

Asymptotics of linear recurrences. Anal. Appl. (Singap.) 12 (4), pp. 463–484.

ⓘ

External Links:

ISSN 0219-5305, Document, Link, MathReview Entry, ZentralBlatt

Referenced by:

§2.9(iii), §2.9(iii).

Encodings:

BibTeX

…

18: 3.11 Approximation Techniques

… ►

Laplace Transform Inversion

… ►More generally, let $f(x)$ be approximated by a linear combination … ►

Example. The Discrete Fourier Transform

… ►is called a discrete Fourier transform pair. ►

The Fast Fourier Transform

…

19: Bibliography D

… ►

Complex zeros of linear combinations of spherical Bessel functions and their derivatives. SIAM J. Math. Anal. 4 (1), pp. 128–133.

ⓘ

External Links:

ISSN 1095-7154, Document, MathReview (C. J. Bouwkamp), ZentralBlatt

Referenced by:

§10.58.

Encodings:

BibTeX

… ►

Computing spectra of linear operators using the Floquet-Fourier-Hill method. J. Comput. Phys. 219 (1), pp. 296–321.

ⓘ

External Links:

ISSN 0021-9991, MathReview, ZentralBlatt

Referenced by:

§22.11.

Encodings:

BibTeX

… ►

Theta functions and non-linear equations. Uspekhi Mat. Nauk 36 (2(218)), pp. 11–80 (Russian).

ⓘ

Notes:

With an appendix by I. M. Krichever. In Russian. English translation: Russian Math. Surveys 36(1981), no. 2, pp. 11–92 (1982)

External Links:

ISSN 0042-1316, Document, MathReview (Alexander A. Pankov), ZentralBlatt

Referenced by:

§21.1, §21.6(ii), §21.7(i), Figure 21.9.2, Figure 21.9.2, §21.9, §21.9, Sidebar 21.SB2, Ch.21, Notations T.

Encodings:

BibTeX

… ►

Convergent expansions for solutions of linear ordinary differential equations having a simple turning point, with an application to Bessel functions. Stud. Appl. Math. 107 (3), pp. 293–323.

ⓘ

External Links:

ISSN 0022-2526, Document, MathReview, ZentralBlatt

Referenced by:

§10.20(ii), §2.8(i).

Encodings:

BibTeX

… ►

Olver’s error bound methods applied to linear ordinary differential equations having a simple turning point. Anal. Appl. (Singap.) 12 (4), pp. 385–402.

ⓘ

External Links:

ISSN 0219-5305, Document, Link, MathReview (Thomas Mbah Acho), ZentralBlatt

Referenced by:

5th item, §14.32.

Encodings:

BibTeX

…

20: Bibliography

… ►

Exact linearization of a Painlevé transcendent. Phys. Rev. Lett. 38 (20), pp. 1103–1106.

ⓘ

External Links:

Document, MathReview (Mark Adler)

Referenced by:

§32.11(ii), §32.13(i), §32.13(ii), §32.13(iii), §32.5.

Encodings:

BibTeX

►

Solitons and the Inverse Scattering Transform. SIAM Studies in Applied Mathematics, Vol. 4, Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA.

ⓘ

External Links:

ISBN 0-89871-174-6, MathReview (Benno Fuchssteiner), ZentralBlatt

Referenced by:

§21.9, §21.9, §32.5, §9.16, Profile Mark J. Ablowitz.

Encodings:

BibTeX

… ►

Lectures on Integral Transforms. Translations of Mathematical Monographs, Vol. 70, American Mathematical Society, Providence, RI.

ⓘ

Notes:

Translated from the Russian by H. H. McFaden

External Links:

ISBN 0-8218-4524-1, MathReview, ZentralBlatt

Referenced by:

§10.22(v).

Encodings:

BibTeX

… ►

Summations and transformations for basic Appell series. J. London Math. Soc. (2) 4, pp. 618–622.

ⓘ

External Links:

MathReview (R. N. Jain), ZentralBlatt

Referenced by:

§17.11.

Encodings:

BibTeX

… ►

Linear algebra done right. Third edition, Undergraduate Texts in Mathematics, Springer, Cham.

ⓘ

External Links:

ISBN 978-3-319-11079-0; 978-3-319-11080-6, Document, Link, MathReview Entry

Referenced by:

§1.2(v), §1.2(vi), §1.3(iv).

Encodings:

BibTeX

…