triconfluent Heun equation

SearchAdvancedHelp

(0.002 seconds)

21—30 of 453 matching pages

21: 31.10 Integral Equations and Representations

§31.10 Integral Equations and Representations

… ►

Kernel Functions

… ►

Kernel Functions

… ►For integral equations for special confluent Heun functions (§31.12) see Kazakov and Slavyanov (1996).

22: Brian D. Sleeman

… ► thesis was Some Boundary Value Problems Associated with the Heun Equation. … ► Plank) of Differential equations and mathematical biology, published by CRC Press in 2003, with a second edition in 2010. … ►

31 Heun Functions

…

23: 31.14 General Fuchsian Equation

§31.14 General Fuchsian Equation

►

§31.14(i) Definitions

… ►Heun’s equation (31.2.1) corresponds to $N=3$. ►

Normal Form

… ►The algorithm returns a list of solutions if they exist. …

24: 31.8 Solutions via Quadratures

§31.8 Solutions via Quadratures

… ►Here ${\mathrm{\Psi }}_{g,N}(\lambda ,z)$ is a polynomial of degree $g$ in $\lambda$ and of degree $N=m_0+m_1+m_2+m_3$ in $z$, that is a solution of the third-order differential equation satisfied by a product of any two solutions of Heun’s equation. …Lastly, ${\lambda }_j$, $j=1,2,\mathrm{\dots },2g+1$, are the zeros of the Wronskian of $w_{+}(𝐦;\lambda ;z)$ and $w_{-}(𝐦;\lambda ;z)$. … ►For $𝐦=(m_0,0,0,0)$, these solutions reduce to Hermite’s solutions (Whittaker and Watson (1927, §23.7)) of the Lamé equation in its algebraic form. …For more details see Smirnov (2002). …

25: 31.11 Expansions in Series of Hypergeometric Functions

§31.11 Expansions in Series of Hypergeometric Functions

… ►Let $w(z)$ be any Fuchs–Frobenius solution of Heun’s equation. … ►Every Fuchs–Frobenius solution of Heun’s equation (31.2.1) can be represented by a series of Type I. … ►

§31.11(v) Doubly-Infinite Series

… ►

26: 31 Heun Functions

Chapter 31 Heun Functions

…

27: 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

… ►

Asymptotic and numeric study of eigenvalues of the double confluent Heun equation. J. Phys. A 31 (42), pp. 8521–8531.

ⓘ

External Links:

ISSN 0305-4470, Document, MathReview, ZentralBlatt

Referenced by:

§31.13, §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

►

Heun’s equation with nearby singularities. Proc. Roy. Soc. London Ser. A 455, pp. 4347–4361.

ⓘ

External Links:

ISSN 1364-5021, Document, MathReview, ZentralBlatt

Referenced by:

§31.13, §31.17(ii).

Encodings:

BibTeX

… ►

The second Painlevé equation. Differ. Uravn. 7 (6), pp. 1124–1125 (Russian).

ⓘ

Notes:

In Russian. English translation: Differential Equations 7(6), pp. 853–854

External Links:

MathReview (Z. Rubinstein), ZentralBlatt

Referenced by:

§32.7(ii).

Encodings:

BibTeX

…

28: Bibliography K

… ►

Hypergeometric expansions of Heun polynomials. SIAM J. Math. Anal. 22 (5), pp. 1450–1459.

ⓘ

External Links:

ISSN 0036-1410, Document, MathReview (Peter A. McCoy), ZentralBlatt

Referenced by:

§31.16(ii).

Encodings:

BibTeX

►

Addendum: “Hypergeometric expansions of Heun polynomials”. SIAM J. Math. Anal. 22 (6), pp. 1803.

ⓘ

External Links:

ISSN 0036-1410, Document, MathReview (Peter A. McCoy), ZentralBlatt

Referenced by:

§31.16(ii).

Encodings:

BibTeX

►

Orthogonal Polynomials on $n$-spheres: Gegenbauer, Jacobi and Heun. In Topics in Polynomials of One and Several Variables and their Applications, pp. 299–322.

ⓘ

External Links:

MathReview, ZentralBlatt

Referenced by:

§31.16(ii).

Encodings:

BibTeX

… ►

Integral equations for special functions of Heun class. Methods Appl. Anal. 3 (4), pp. 447–456.

ⓘ

External Links:

ISSN 1073-2772, FullText, MathReview, ZentralBlatt

Referenced by:

§31.10(ii).

Encodings:

BibTeX

… ►

The Korteweg-de Vries Equation and Related Evolution Equations. In Nonlinear Wave Motion (Proc. AMS-SIAM Summer Sem., Clarkson Coll. Tech., Potsdam, N.Y., 1972), A. C. Newell (Ed.), Lectures in Appl. Math., Vol. 15, pp. 61–83.

ⓘ

External Links:

MathReview (G. L. Lamb, Jr.), ZentralBlatt

Referenced by:

§22.19(iii).

Encodings:

BibTeX

…

29: Bibliography E

… ►

Integral equations for Heun functions. Quart. J. Math., Oxford Ser. 13, pp. 107–112.

ⓘ

External Links:

Document, MathReview (E. Rothe), ZentralBlatt

Referenced by:

§31.10(i).

Encodings:

BibTeX

►

The Fuchsian equation of second order with four singularities. Duke Math. J. 9 (1), pp. 48–58.

ⓘ

External Links:

Document, MathReview (R. E. Langer), ZentralBlatt

Referenced by:

§31.11(i).

Encodings:

BibTeX

►

Certain expansions of solutions of the Heun equation. Quart. J. Math., Oxford Ser. 15, pp. 62–69.

ⓘ

External Links:

Document, MathReview (R. E. Langer), ZentralBlatt

Referenced by:

§31.11(i), §31.11(i), §31.9(i).

Encodings:

BibTeX

… ►

A catalogue of Sturm-Liouville differential equations. In Sturm-Liouville theory, pp. 271–331.

ⓘ

External Links:

Document, Link, MathReview Entry

Referenced by:

§1.18(ix), §1.18(x).

Encodings:

BibTeX

…

30: Bibliography S

… ►

Structure of avoided crossings for eigenvalues related to equations of Heun’s class. J. Phys. A 30 (2), pp. 673–687.

ⓘ

External Links:

ISSN 0305-4470, Document, MathReview (Éric Delabaere), ZentralBlatt

Referenced by:

§31.13.

Encodings:

BibTeX

… ►

Some Boundary Value Problems Associated with the Heun Equation. Ph.D. Thesis, London University.

ⓘ

Notes:

Available from the library, University of Surrey, UK

External Links:

LibraryRecord

Referenced by:

§31.9(i), §31.9(ii), Ch.31, Profile Brian D. Sleeman.

Encodings:

BibTeX

… ►

Non-linear integral equations for Heun functions. Proc. Edinburgh Math. Soc. (2) 16, pp. 281–289.

ⓘ

External Links:

Document, MathReview (J. D. DePree), ZentralBlatt

Referenced by:

§31.10(ii).

Encodings:

BibTeX

… ►

Elliptic Solitons and Heun’s Equation. In The Kowalevski Property (Leeds, UK, 2000), V. B. Kuznetsov (Ed.), CRM Proc. Lecture Notes, Vol. 32, pp. 287–306.

ⓘ

External Links:

MathReview, ZentralBlatt

Referenced by:

§31.8.

Encodings:

BibTeX

… ►

Perturbations of Kerr-de Sitter black holes and Heun’s equations. Progr. Theoret. Phys. 100 (3), pp. 491–505.

ⓘ

External Links:

ISSN 0033-068X, FullText, MathReview (Volker Perlick)

Referenced by:

§31.17(ii).

Encodings:

BibTeX

…