relation%20to%20Heun%20equation

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1: Bibliography M

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Hill’s Equation. Interscience Tracts in Pure and Applied Mathematics, No. 20, Interscience Publishers John Wiley & Sons, New York-London-Sydney.

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Notes:

Reprinted by Dover Publications, Inc., New York, 1979.

External Links:

MathReview (H. Hochstadt), ZentralBlatt

Referenced by:

§1.3(iii), §28.29(i), §28.29(ii), §28.29(ii), §28.29(iii), §28.29(iii), §28.29(iii), §28.30(i), Ch.28, §29.3(i), §29.9.

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On reducing the Heun equation to the hypergeometric equation. J. Differential Equations 213 (1), pp. 171–203.

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ISSN 0022-0396, Document, MathReview (Wolfgang Bühring), ZentralBlatt

Referenced by:

§31.7(i).

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The 192 solutions of the Heun equation. Math. Comp. 76 (258), pp. 811–843.

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ISSN 0025-5718, Document, MathReview (Wadim Zudilin), ZentralBlatt (Masaaki Yoshida)

Referenced by:

§31.3(iii).

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Picard and Chazy solutions to the Painlevé VI equation. Math. Ann. 321 (1), pp. 157–195.

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ISSN 0025-5831, Document, MathReview, ZentralBlatt

Referenced by:

§32.9(iii).

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A new symmetry related to $\mathrm{𝑆𝑈}(n)$ for classical basic hypergeometric series. Adv. in Math. 57 (1), pp. 71–90.

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ISSN 0001-8708, Document, MathReview (George E. Andrews), ZentralBlatt

Referenced by:

§17.15.

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2: Bibliography B

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Tables Relating to the Radial Mathieu Functions. Vol. 1: Functions of the First Kind. U.S. Government Printing Office, Washington, D.C..

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External Links:

MathReview (C. J. Bouwkamp)

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1st item.

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Tables Relating to the Radial Mathieu Functions. Vol. 2: Functions of the Second Kind. U.S. Government Printing Office, Washington, D.C..

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External Links:

MathReview (C. J. Bouwkamp)

Referenced by:

2nd item, 1st item.

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Bessel functions and modular relations of higher type and hyperbolic differential equations. Comm. Sém. Math. Univ. Lund [Medd. Lunds Univ. Mat. Sem.] 1952 (Tome Supplementaire), pp. 12–20.

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External Links:

MathReview (S. C. van Veen), ZentralBlatt

Referenced by:

§35.5(i).

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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.

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ISSN 0305-4470, Document, MathReview, ZentralBlatt

Referenced by:

§31.13.

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The double confluent Heun equation: Characteristic exponent and connection formulae. Methods Appl. Anal. 1 (3), pp. 348–370.

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ISSN 1073-2772, FullText, MathReview (W. Balser), ZentralBlatt

Referenced by:

§31.12.

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3: Bibliography F

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Asymptotics of the spectrum of the Heun equation and of Heun functions. Izv. Akad. Nauk SSSR Ser. Mat. 55 (3), pp. 631–646 (Russian).

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Notes:

In Russian. English translation: Math. USSR-Izv., 38(1992), no. 3, pp. 621–635 (1992)

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ISSN 0373-2436, Document, MathReview (Andreĭ Bolibrukh), ZentralBlatt

Referenced by:

§31.13.

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Numerical calculation of singular integrals related to Hankel transform. Comput. Math. Appl. 21 (2-3), pp. 87–94.

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Notes:

Fortran, minimum precision 6D.

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ISSN 0898-1221, Document, MathReview, ZentralBlatt

Referenced by:

§10.77(ix).

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On a unified approach to transformations and elementary solutions of Painlevé equations. J. Math. Phys. 23 (11), pp. 2033–2042.

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ISSN 0022-2488, Document, MathReview (Hélène Airault), ZentralBlatt

Referenced by:

§32.13(i), §32.7(i), §32.7(iii).

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From continuous to discrete Painlevé equations. J. Math. Anal. Appl. 180 (2), pp. 342–360.

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ISSN 0022-247X, Document, MathReview (Evangelos Ifantis), ZentralBlatt

Referenced by:

§32.7(ii).

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Application of the $\tau$-function theory of Painlevé equations to random matrices: PIV, PII and the GUE. Comm. Math. Phys. 219 (2), pp. 357–398.

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ISSN 0010-3616, Document, MathReview (Alexei Khorunzhy), ZentralBlatt

Referenced by:

§32.10(iv), §32.14, §32.6(v).

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4: Bibliography S

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

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

Referenced by:

§31.13.

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

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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.

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

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

Referenced by:

§31.10(ii).

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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.

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External Links:

MathReview, ZentralBlatt

Referenced by:

§31.8.

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

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

Referenced by:

§31.17(ii).

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5: Bibliography D

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Formes canoniques des équations confluentes de l’équation de Heun. Ann. Soc. Sci. Bruxelles Sér. I 92 (1-2), pp. 53–78.

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External Links:

MathReview (A. E. Danese), ZentralBlatt

Referenced by:

§31.12.

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Sur les équations confluentes de l’équation de Heun. Ann. Soc. Sci. Bruxelles Sér. I 92 (3), pp. 151–189.

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ISSN 0037-959X, MathReview, ZentralBlatt

Referenced by:

§31.12.

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Convergent Liouville-Green expansions for second-order linear differential equations, with an application to Bessel functions. Proc. Roy. Soc. London Ser. A 440, pp. 37–54.

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ISSN 0962-8444, FullText, MathReview (W. Balser), ZentralBlatt

Referenced by:

§10.41(iii), §2.8(i).

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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.

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ISSN 0022-2526, Document, MathReview, ZentralBlatt

Referenced by:

§10.20(ii), §2.8(i).

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

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

Referenced by:

5th item, §14.32.

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