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1: DLMF Project News

error generating summary

2: Publications

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Boundary/Contour Fitted Grid Generation for Effective Visualizations in a Digital Library of Mathematical Functions, Proceedings of the 9th International Conference on Numerical Grid Generation in Computational Field Simulations, San Jose, June 11–18, 2005. pp. 61–71.

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Web-Based 3D Visualization in a Digital Library of Mathematical Functions, Proceedings of the Web3D Symposium, Bangor, UK, March 29–April 1, 2005.

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From B-Spline Mesh Generation to Effective Visualizations for the NIST Digital Library of Mathematical Functions, in Curve and Surface Design, Proceedings of the Sixth International Conference on Curves and Surfaces, Avignon, France June 29–July 5, 2006, pp. 235–243.

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NIST’s Digital Library of Mathematial Functions, Physics Today 71, 2, 48 (2018), pp. 48–53.

3: Antony Ross Barnett

… ► 2018) was Senior Research Fellow in the Mathematics Department, University of Waikato, Hamilton, New Zealand. …

4: Bibliography N

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Error bounds for the large-argument asymptotic expansions of the Lommel and allied functions. Stud. Appl. Math. 140 (4), pp. 508–541.

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External Links:

ISSN 0022-2526, Document, Link, MathReview (Pedro J. Pagola), ZentralBlatt

Referenced by:

§11.11(i), §11.11(i).

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Elliptic integrals of the second and third kinds. Zastos. Mat. 11, pp. 99–102.

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Notes:

Includes Algol program.

External Links:

MathReview

Referenced by:

§19.39(iii).

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On the calculation of elliptic integrals of the second and third kinds. Zastos. Mat. 11, pp. 91–94.

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External Links:

MathReview, ZentralBlatt

Referenced by:

§19.36(ii).

Encodings:

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COULN, a program for evaluating negative energy Coulomb functions. Comput. Phys. Comm. 33 (4), pp. 413–419.

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Notes:

Double-precision Fortran code.

External Links:

Document, Code

Referenced by:

2nd item, 7th item.

Encodings:

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Symmetries in the fourth Painlevé equation and Okamoto polynomials. Nagoya Math. J. 153, pp. 53–86.

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External Links:

ISSN 0027-7630, MathReview (Andrei A. Kapaev), ZentralBlatt

Referenced by:

§32.8(iv).

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5: Bibliography K

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Bernstein, Pick, Poisson and related integral expressions for Lambert $W$ . Integral Transforms Spec. Funct. 23 (11), pp. 817–829.

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ISSN 1065-2469, Document, Link, MathReview (Ross C. McPhedran), ZentralBlatt

Referenced by:

§4.13.

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Auxiliary table for the incomplete elliptic integrals. J. Math. Physics 27, pp. 11–36.

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External Links:

MathReview (S. C. van Veen), ZentralBlatt

Referenced by:

§19.12.

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Algorithm 327: Dilogarithm [S22]. Comm. ACM 11 (4), pp. 270–271.

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Notes:

Includes Algol program, maximum accuracy 12D.

External Links:

ISSN 0001-0782, Document

Referenced by:

§25.21(v).

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Dualities in the $q$-Askey scheme and degenerate DAHA. Stud. Appl. Math. 141 (4), pp. 424–473.

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External Links:

ISSN 0022-2526, Document, Link, MathReview (Marzena Szajewska)

Referenced by:

(18.28.1_5).

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Jacobi polynomials, Bernstein-type inequalities and dispersion estimates for the discrete Laguerre operator. Adv. Math. 333, pp. 796–821.

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External Links:

ISSN 0001-8708, Document, Link, MathReview (Martin Axel Hallnäs)

Referenced by:

§18.14(i).

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6: Bibliography I

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IEEE Standard for Interval Arithmetic: IEEE Std 1788.1-2017. The Institute of Electrical and Electronics Engineers, Inc..

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External Links:

ISBN 978-1-5044-4602-0, Document

Referenced by:

§3.1(ii), §3.1(ii), Erratum (V1.0.25) for Section 3.1.

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The zeros of regular Coulomb wave functions and of their derivatives. Math. Comp. 29, pp. 878–887.

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External Links:

ISSN 0025-5718, Document, MathReview, ZentralBlatt

Referenced by:

§3.8(iii).

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An integral which occurs in statistics. Proceedings of the Cambridge Philosophical Society 29, pp. 271–276.

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External Links:

Document, ZentralBlatt

Referenced by:

§35.3(i), §35.3(ii).

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7: 3.1 Arithmetics and Error Measures

… ►In the case of the normalized binary interchange formats, the representation of data for binary32 (previously single precision) ($N=32$, $p=24$, $E_{\min }=-126$, $E_{\max }=127$), binary64 (previously double precision) ($N=64$, $p=53$, $E_{\min }=-1022$, $E_{\max }=1023$) and binary128 (previously quad precision) ($N=128$, $p=113$, $E_{\min }=-16382$, $E_{\max }=16383$) are as in Figure 3.1.1. … ►For interval arithmetic, one should refer to the IEEE Standards for Interval Arithmetic IEEE (2015, 2018). …

8: Bibliography R

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Uniform asymptotic approximations to the solutions of the Orr-Sommerfeld equation. I. Plane Couette flow. Studies in Appl. Math. 53, pp. 91–110.

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External Links:

MathReview (T. W. Kao), ZentralBlatt

Referenced by:

§2.8(iii).

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Uniform asymptotic approximations to the solutions of the Orr-Sommerfeld equation. II. The general theory. Studies in Appl. Math. 53, pp. 217–224.

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External Links:

MathReview (T. W. Kao), ZentralBlatt

Referenced by:

§2.8(iii).

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Universality properties of Gaussian quadrature, the derivative rule, and a novel approach to Stieltjes inversion.

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Notes:

arXiv:1812.02196

Referenced by:

§18.40(ii).

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On the zeros of the hypergeometric function. Math. Ann. 191 (1), pp. 53–58.

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External Links:

ISSN 0025-5831, Document, MathReview (R. C. Varma), ZentralBlatt

Referenced by:

§15.13.

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9: Bibliography C

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Note on Nörlund’s polynomial $B_n^{(z)}$ . Proc. Amer. Math. Soc. 11 (3), pp. 452–455.

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External Links:

FullText, MathReview (M. P. Drazin), ZentralBlatt

Referenced by:

§26.1, §26.1, Notations S, Notations S.

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Properties of generalized Freud polynomials. J. Approx. Theory 225, pp. 148–175.

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External Links:

ISSN 0021-9045, Document, Link, MathReview (Maria das Neves Rebocho)

Referenced by:

§18.32.

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The fourth Painlevé equation and associated special polynomials. J. Math. Phys. 44 (11), pp. 5350–5374.

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External Links:

ISSN 0022-2488, Document, MathReview, ZentralBlatt

Referenced by:

§32.8(iv).

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Further formulas for calculating approximate values of the zeros of certain combinations of Bessel functions. IEEE Trans. Microwave Theory Tech. 11 (6), pp. 546–547.

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External Links:

ISSN 0018-9480, FullText

Referenced by:

§10.21(x).

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

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External Links:

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

Referenced by:

§13.29(v), §15.19(v).

Encodings:

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10: 18.32 OP’s with Respect to Freud Weights

… ►The special case $Q(x)=\frac{1}{4}{x}^4-t{x}^2$ is of particular interest, see Clarkson and Jordaan (2018). …