modified%20Bessel%20equation

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11: Bibliography S

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Transformations of the Jacobian amplitude function and its calculation via the arithmetic-geometric mean. SIAM J. Math. Anal. 20 (6), pp. 1514–1528.

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ISSN 0036-1410, Document, MathReview (J. M. H. Peters), ZentralBlatt

Referenced by:

§22.19(i), §22.20(vi).

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A code to evaluate modified Bessel functions based on the continued fraction method. Comput. Phys. Comm. 105 (2-3), pp. 263–272.

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ISSN 0010-4655, Document, Code, MathReview, ZentralBlatt

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7th item.

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Bounds for ratios of modified Bessel functions and associated Turán-type inequalities. J. Math. Anal. Appl. 374 (2), pp. 516–528.

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ISSN 0022-247X, Document, FullText, MathReview (Beyza Caliskan Aslan), ZentralBlatt

Referenced by:

§10.37, §10.37.

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Uniform asymptotic forms of modified Mathieu functions. Quart. J. Mech. Appl. Math. 20 (3), pp. 365–380.

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Document, MathReview (F. W. J. Olver), ZentralBlatt

Referenced by:

§28.8(iv).

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On the calculation of complex zeros of the modified Bessel function of the second kind. Dokl. Akad. Nauk SSSR 280 (2), pp. 296–299.

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Notes:

English translation in Soviet Math. Dokl. 31(1), pp. 78–81

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ISSN 0002-3264, MathReview (I. F. Kushnirchuk), ZentralBlatt

Referenced by:

§10.74(vi).

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12: Bibliography W

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The Nahm equations, finite-gap potentials and Lamé functions. J. Phys. A 20 (10), pp. 2679–2683.

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ISSN 0305-4470, Document, MathReview (James M. D’Archangelo), ZentralBlatt

Referenced by:

§29.19(ii).

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A Treatise on the Theory of Bessel Functions. 2nd edition, Cambridge University Press, Cambridge, England.

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Notes:

Reprinted in 1995.

External Links:

MathReview (G. Szegő), ZentralBlatt

Referenced by:

§1.13(v), §10.1, §10.10, §10.12, §10.13, §10.14, §10.14, §10.15, §10.16, §10.17(iii), §10.18(iii), §10.19(ii), §10.19(iii), §10.2(ii), §10.21(i), §10.21(i), §10.21(ii), §10.21(iii), §10.21(iv), §10.21(vi), §10.21(xiii), (10.22.72), (10.22.78), §10.22(i), §10.22(ii), §10.22(iv), §10.22(vi), §10.23(iii), §10.23(iii), §10.23(iii), §10.23(i), §10.23(ii), §10.23(iii), §10.27, §10.29(i), §10.29(ii), §10.31, §10.32(i), §10.32(ii), §10.32(iii), §10.32(iv), §10.34, §10.4, §10.40(i), §10.40(ii), §10.42, §10.42, §10.43(iv), §10.43(vi), §10.44(ii), §10.54, §10.6(i), §10.6(ii), §10.60(iii), §10.60(iv), §10.8, (10.9.26), §10.9(i), §10.9(ii), §10.9(iii), §10.9(iv), Ch.10, §11.10(i), §11.10(ii), §11.10(iii), §11.10(ix), §11.10(v), §11.10(vi), (11.11.10), (11.11.18), (11.11.19), (11.11.8), §11.11(i), §11.11(iii), §11.2(i), §11.2(ii), §11.4(ii), §11.4(v), §11.5(i), §11.5(iii), §11.6(i), §11.6(iii), §11.6(iii), §11.6(iii), §11.7(ii), §11.9(i), §11.9(iii), §11.9(iv), Ch.11, §18.17(v), §2.5(i), Erratum (V1.0.21) for Equation (10.22.72).

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Rational approximations for the modified Bessel function of the second kind. Comput. Phys. Comm. 59 (3), pp. 471–493.

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ISSN 0010-4655, Document, MathReview, ZentralBlatt

Referenced by:

§10.76(ii).

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Tables of Summable Series and Integrals Involving Bessel Functions. Holden-Day, San Francisco, CA.

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External Links:

MathReview, ZentralBlatt

Referenced by:

§10.22(vi), §10.23(iv), §10.43(vi).

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Algorithm 44: Bessel functions computed recursively. Comm. ACM 4 (4), pp. 177–178.

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Notes:

Includes Algol code, maximum accuracy 8S.

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ISSN 0001-0782, Document

Referenced by:

§10.77(ii).

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13: Bibliography L

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Bounds for modified Bessel functions. J. Comput. Appl. Math. 34 (3), pp. 263–267.

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ISSN 0377-0427, Document, MathReview (N. Hayek Calil), ZentralBlatt

Referenced by:

§10.37.

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Algorithm 917: complex double-precision evaluation of the Wright $\omega$ function. ACM Trans. Math. Software 38 (3), pp. Art. 20, 17.

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ISSN 0098-3500, Document, FullText, MathReview Entry, ZentralBlatt

Referenced by:

§4.13, 2nd item, §4.48(iv).

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An asymptotic estimate for the Bernoulli and Euler numbers. Canad. Math. Bull. 20 (1), pp. 109–111.

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MathReview (D. H. Lehmer), ZentralBlatt

Referenced by:

§24.11.

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An application of the finite element approximation method to find the complex zeros of the modified Bessel function $K_n(z)$ . Math. Comp. 33 (148), pp. 1299–1306.

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ISSN 0025-5718, FullText, MathReview (R. P. Boas, Jr.), ZentralBlatt

Referenced by:

§10.74(vi), 2nd item.

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

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Notes:

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

External Links:

MathReview (Z. Rubinstein), ZentralBlatt

Referenced by:

§32.7(ii).

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14: Bibliography V

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Accurate calculation of the modified Mathieu functions of integer order. Quart. Appl. Math. 65 (1), pp. 1–23.

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Notes:

For software, see Van Buren (website)

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ISSN 0033-569X, MathReview (Javier Segura), ZentralBlatt

Referenced by:

§28.36(iii).

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Integrating products of Bessel functions with an additional exponential or rational factor. Comput. Phys. Comm. 178 (8), pp. 578–590.

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Notes:

Associated computer program available online

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ISSN 0010-4655, Document, FullText, MathReview Entry, ZentralBlatt

Referenced by:

§10.74(vii), §10.74(vii).

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Some novel infinite series of spherical Bessel functions. Quart. Appl. Math. 42 (3), pp. 321–324.

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ISSN 0033-569X, MathReview (A. de Castro Brzezicki), ZentralBlatt

Referenced by:

§10.60(iii), §10.60(iii).

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Error estimates for Rayleigh-Ritz approximations of eigenvalues and eigenfunctions of the Mathieu and spheroidal wave equation. Constr. Approx. 20 (1), pp. 39–54.

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ISSN 0176-4276, Document, MathReview, ZentralBlatt

Referenced by:

§30.16(i), §30.16(ii), §30.16(ii).

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On the rational solutions of the second Painlevé equation. Differ. Uravn. 1 (1), pp. 79–81 (Russian).

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Notes:

In Russian. English translation: Differential Equations 1(1), pp. 58–59.

External Links:

MathReview, ZentralBlatt

Referenced by:

§32.8(ii).

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