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11: Bibliography D

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Complex zeros of cylinder functions. Math. Comp. 20 (94), pp. 215–222.

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Notes:

For a numerical error in one of the zeros see Amos (1985).

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ISSN 0025-5718, FullText, MathReview, ZentralBlatt

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2nd item.

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

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Notes:

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

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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.

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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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Uniform asymptotic expansions for Whittaker’s confluent hypergeometric functions. SIAM J. Math. Anal. 20 (3), pp. 744–760.

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Notes:

(This reference has several typographical errors.)

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ISSN 0036-1410, Document, MathReview (F. W. J. Olver), ZentralBlatt

Referenced by:

§13.21(ii), §13.21(iii), §13.21(iv).

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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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12: Bibliography L

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Some differential equations and associated integral equations. Quart. J. Math. (Oxford) 5, pp. 81–97.

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External Links:

Document, ZentralBlatt

Referenced by:

§31.10(i), §31.9(i).

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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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Some Differential Equations Satisfied by Hypergeometric Functions. In Approximation and Computation (West Lafayette, IN, 1993), Internat. Ser. Numer. Math., Vol. 119, pp. 371–381.

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MathReview (M. E. Muldoon), ZentralBlatt

Referenced by:

§16.8(ii).

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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

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MathReview (Z. Rubinstein), ZentralBlatt

Referenced by:

§32.7(ii).

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13: 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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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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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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A Maple package for symmetric functions. J. Symbolic Comput. 20 (5-6), pp. 755–768.

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Notes:

For software see John Stembridge’s home page. The SF package contains Maple software for zonal, Jack, and Macdonald polynomials.

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Home Page, ISSN 0747-7171, Document, MathReview, ZentralBlatt

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3rd item.

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Numerical Methods Based on Sinc and Analytic Functions. Springer Series in Computational Mathematics, Vol. 20, Springer-Verlag, New York.

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Notes:

Sinc-Pack, a set of 480 Matlab programs with a 470-page tutorial, is available for purchase from SINC, LLC by contacting Frank Stenger.

External Links:

ISBN 0-387-94008-1, MathReview (B. Boyanov), ZentralBlatt

Referenced by:

§3.3(vi), §3.4(i), §3.5(i).

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14: Bibliography V

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A Mathieu equation for ships rolling among waves. I, II. Norske Vid. Selsk. Forh., Trondheim 22 (25–26), pp. 113–123.

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MathReview (J. V. Wehausen), ZentralBlatt

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2nd item.

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On the growth of convergence radii for the eigenvalues of the Mathieu equation. Math. Nachr. 192, pp. 239–253.

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ISSN 0025-584X, Document, MathReview (M. E. Muldoon), ZentralBlatt

Referenced by:

§28.6(i).

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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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Four remarks on eigenvalues of Lamé’s equation. Anal. Appl. (Singap.) 2 (2), pp. 161–175.

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ISSN 0219-5305, Document, MathReview, ZentralBlatt

Referenced by:

§29.3(ii), §29.3(vii), §29.5, §29.7(i), §29.7(i).

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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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15: Bibliography N

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Toda equation and its solutions in special functions. J. Phys. Soc. Japan 65 (6), pp. 1589–1597.

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ISSN 0031-9015, Document, MathReview, ZentralBlatt

Referenced by:

§18.38(ii).

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On an integral transform involving a class of Mathieu functions. SIAM J. Math. Anal. 20 (6), pp. 1500–1513.

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ISSN 0036-1410, Document, MathReview (K. C. Gupta), ZentralBlatt

Referenced by:

§28.26(ii).

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Reduction and evaluation of elliptic integrals. Math. Comp. 20 (94), pp. 223–231.

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FullText, MathReview (I. A. Stegun), ZentralBlatt

Referenced by:

§19.37(iv).

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A table of integrals of the error functions. J. Res. Nat. Bur. Standards Sect B. 73B, pp. 1–20.

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Notes:

See for additions and corrections same journal, Sect. B 75, 149–163 (1975)

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MathReview, ZentralBlatt

Referenced by:

§7.14(iii), §7.21, §7.7(iii).

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Tables of Generalized Airy Functions for the Asymptotic Solution of the Differential Equations $ϵ{(p{y}^{\prime })}^{\prime }+(q+ϵr)y=f$ . Pergamon Press, Oxford.

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Notes:

D. E. Brown, translator.

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MathReview, ZentralBlatt

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4th item.

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16: Bibliography C

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Special Functions of Applied Mathematics. Academic Press, New York.

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External Links:

ISBN 0-12-160150-1, MathReview, ZentralBlatt

Referenced by:

(19.16.2_5), §19.16(ii), §19.16(ii), §19.16(iii), §19.18(i), §19.18(ii), §19.2(iv), §19.20(i), §19.20(iv), §19.20(v), §19.21(ii), §19.21(ii), §19.23, §19.25(i), §19.26(i), §19.26(iii), §19.28, §19.30(i), §19.30(ii), §19.30(iii), §19.32, §19.33(i), §19.33(ii), §19.33(iv), §19.34, Ch.19, §5.12, §5.6(ii), Ch.5, Profile Bille C. Carlson, Erratum (V1.0.18) for Equation (19.16.9).

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Asymptotic estimates for generalized Stirling numbers. Analysis (Munich) 20 (1), pp. 1–13.

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ISSN 0174-4747, MathReview (F. T. Howard), ZentralBlatt

Referenced by:

§26.8(vii).

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Painlevé Equations—Nonlinear Special Functions: Computation and Application. In Orthogonal Polynomials and Special Functions, F. Marcellàn and W. van Assche (Eds.), Lecture Notes in Math., Vol. 1883, pp. 331–411.

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ISBN 3-540-31062-2, MathReview (Marta Mazzocco), ZentralBlatt

Referenced by:

Ch.32.

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Validated computation of certain hypergeometric functions. ACM Trans. Math. Software 38 (2), pp. Art. 11, 20.

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

Referenced by:

§13.29(v), §15.19(v).

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Coulomb effects in the Klein-Gordon equation for pions. Phys. Rev. C 20 (2), pp. 696–704.

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External Links:

Document

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5th item.

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17: 9.7 Asymptotic Expansions

§9.7 Asymptotic Expansions

… ►Numerical values of $\chi (n)$ are given in Table 9.7.1 for $n=1(1)20$ to 2D. … ►

§9.7(iii) Error Bounds for Real Variables

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§9.7(iv) Error Bounds for Complex Variables

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18: Bibliography K

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

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External Links:

ISSN 1073-2772, FullText, MathReview, ZentralBlatt

Referenced by:

§31.10(ii).

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Algorithm 737: INTLIB: A portable Fortran 77 interval standard-function library. ACM Trans. Math. Software 20 (4), pp. 447–459.

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ISSN 0098-3500, Document, GAMS (module 737; package TOMS), ZentralBlatt

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1st item.

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Methods of computing the Riemann zeta-function and some generalizations of it. USSR Comput. Math. and Math. Phys. 20 (6), pp. 212–230.

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Document, MathReview (Matti Jutila), ZentralBlatt

Referenced by:

§25.18(i).

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Connection formulae for asymptotics of solutions of the degenerate third Painlevé equation. I. Inverse Problems 20 (4), pp. 1165–1206.

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ISSN 0266-5611, Document, MathReview (Shun Shimomura), ZentralBlatt

Referenced by:

§32.11(iv).

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The Askey scheme as a four-manifold with corners. Ramanujan J. 20 (3), pp. 409–439.

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ISSN 1382-4090, Document, FullText, MathReview (José Luis López), ZentralBlatt

Referenced by:

§18.26(v), §18.26(v).

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19: Bibliography O

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On the $\tau$-function of the Painlevé equations. Phys. D 2 (3), pp. 525–535.

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ISSN 0167-2789, Document, MathReview (D. A. Lutz), ZentralBlatt

Referenced by:

§32.6(i), §32.6(ii).

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An error analysis of the modified Clenshaw method for evaluating Chebyshev and Fourier series. J. Inst. Math. Appl. 20 (3), pp. 379–391.

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Document, MathReview (David L. Elliott), ZentralBlatt

Referenced by:

§3.11(ii).

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A new method for the evaluation of zeros of Bessel functions and of other solutions of second-order differential equations. Proc. Cambridge Philos. Soc. 46 (4), pp. 570–580.

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Document, MathReview (J. Todd), ZentralBlatt

Referenced by:

§10.21(ii).

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On the asymptotic solution of second-order differential equations having an irregular singularity of rank one, with an application to Whittaker functions. J. Soc. Indust. Appl. Math. Ser. B Numer. Anal. 2 (2), pp. 225–243.

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External Links:

Document, MathReview (T. E. Hull), ZentralBlatt

Referenced by:

§13.19, §13.7(ii).

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Exponentially-improved asymptotic solutions of ordinary differential equations I: The confluent hypergeometric function. SIAM J. Math. Anal. 24 (3), pp. 756–767.

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ISSN 0036-1410, Document, MathReview (Hussain S. Nur), ZentralBlatt

Referenced by:

§10.17(v), §13.7(iii), (9.7.18), (9.7.19), (9.7.20), (9.7.21), (9.7.22), (9.7.23), §9.7(v).

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20: Bibliography G

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Algorithm 726: ORTHPOL — a package of routines for generating orthogonal polynomials and Gauss-type quadrature rules. ACM Trans. Math. Software 20 (1), pp. 21–62.

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Notes:

For remark see same journal 24(1998), p. 355.

External Links:

Document, ISSN 0098-3500, GAMS (module 726; package TOMS), ZentralBlatt

Referenced by:

2nd item, §3.5(v), §3.5(v).

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The Computation of Special Functions by Linear Difference Equations. In Advances in Difference Equations (Veszprém, 1995), S. Elaydi, I. Győri, and G. Ladas (Eds.), pp. 213–243.

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External Links:

ISBN 90-5699-521-9, MathReview, ZentralBlatt

Referenced by:

§3.6(iii), §3.6(vii).

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Algorithm 939: computation of the Marcum Q-function. ACM Trans. Math. Softw. 40 (3), pp. 20:1–20:21.

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Notes:

Includes Fortran program claiming 12S accuracy

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

Referenced by:

3rd item, §10.77(ix).

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Mutual integrability, quadratic algebras, and dynamical symmetry. Ann. Phys. 217 (1), pp. 1–20.

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ISSN 0003-4916, Link, MathReview (A. O. Barut), ZentralBlatt

Referenced by:

§18.38(iii).

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Riccati equations and convolution formulae for functions of Rayleigh type. J. Phys. A 33 (7), pp. 1363–1368.

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ISSN 0305-4470, Document, MathReview, ZentralBlatt

Referenced by:

§10.21(xiii).

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