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1: 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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A Special Functions Handbook for the Digital Age, Notices of the American Mathematical Society 58, 7 (2011), pp. 905–911.

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2: 10 Bessel Functions

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3: 11 Struve and Related Functions

Chapter 11 Struve and Related Functions

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4: Staff

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Richard B. Paris, University of Abertay, Chaps. 8, 11

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Hans Volkmer, University of Wisconsin, Milwaukee, Chaps. 29, 30

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Richard B. Paris, University of Abertay Dundee, for Chaps. 8, 11 (deceased)

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Hans Volkmer, University of Wisconsin–Milwaukee, for Chaps. 29, 30

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5: 29 Lamé Functions

Chapter 29 Lamé Functions

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6: 26.2 Basic Definitions

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Table 26.2.1: Partitions $p\left(n\right)$.

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$n$	$p\left(n\right)$	$n$	$p\left(n\right)$	$n$	$p\left(n\right)$
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6	11	23	1255	40	37338
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11	56	28	3718	45	89134
12	77	29	4565	46	1 05558
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7: 28.6 Expansions for Small $q$

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28.6.2 $$a_1\left(q\right)=1+q-\frac{1}{8}{q}^2-\frac{1}{64}{q}^3-\frac{1}{1536}{q}^4+\frac{11}{36864}{q}^5+\frac{49}{\mathrm{5\hspace{0.33em}89824}}{q}^6+\frac{55}{\mathrm{94\hspace{0.33em}37184}}{q}^7-\frac{83}{\mathrm{353\hspace{0.33em}89440}}{q}^8+\mathrm{\cdots },$$

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Symbols:

$a_n\left(q\right)$: eigenvalues of Mathieu equation and $q=h^2$: parameter

Permalink:

http://dlmf.nist.gov/28.6.E2

Encodings:

pMML, png, TeX

See also:

Annotations for §28.6(i), §28.6 and Ch.28

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28.6.3 $$b_1\left(q\right)=1-q-\frac{1}{8}{q}^2+\frac{1}{64}{q}^3-\frac{1}{1536}{q}^4-\frac{11}{36864}{q}^5+\frac{49}{\mathrm{5\hspace{0.33em}89824}}{q}^6-\frac{55}{\mathrm{94\hspace{0.33em}37184}}{q}^7-\frac{83}{\mathrm{353\hspace{0.33em}89440}}{q}^8+\mathrm{\cdots },$$

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Symbols:

$b_n\left(q\right)$: eigenvalues of Mathieu equation and $q=h^2$: parameter

Permalink:

http://dlmf.nist.gov/28.6.E3

Encodings:

pMML, png, TeX

See also:

Annotations for §28.6(i), §28.6 and Ch.28

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28.6.10 $$a_5\left(q\right)=25+\frac{1}{48}{q}^2+\frac{11}{\mathrm{7\hspace{0.33em}74144}}{q}^4+\frac{1}{\mathrm{1\hspace{0.33em}47456}}{q}^5+\frac{37}{\mathrm{8918\hspace{0.33em}13888}}{q}^6+\mathrm{\cdots },$$

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Symbols:

$a_n\left(q\right)$: eigenvalues of Mathieu equation and $q=h^2$: parameter

Permalink:

http://dlmf.nist.gov/28.6.E10

Encodings:

pMML, png, TeX

See also:

Annotations for §28.6(i), §28.6 and Ch.28

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28.6.11 $$b_5\left(q\right)=25+\frac{1}{48}{q}^2+\frac{11}{\mathrm{7\hspace{0.33em}74144}}{q}^4-\frac{1}{\mathrm{1\hspace{0.33em}47456}}{q}^5+\frac{37}{\mathrm{8918\hspace{0.33em}13888}}{q}^6+\mathrm{\cdots },$$

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Symbols:

$b_n\left(q\right)$: eigenvalues of Mathieu equation and $q=h^2$: parameter

Permalink:

http://dlmf.nist.gov/28.6.E11

Encodings:

pMML, png, TeX

See also:

Annotations for §28.6(i), §28.6 and Ch.28

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28.6.14 $$\begin{array}{c}{a}_m\left(q\right)\\ b_m\left(q\right)\end{array}\}=m^2+\frac{1}{2(m^2-1)}{q}^2+\frac{5m^2+7}{32{(m^2-1)}^3(m^2-4)}{q}^4+\frac{9m^4+58m^2+29}{64{(m^2-1)}^5(m^2-4)(m^2-9)}{q}^6+\mathrm{\cdots }.$$

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Symbols:

$a_n\left(q\right)$: eigenvalues of Mathieu equation, $b_n\left(q\right)$: eigenvalues of Mathieu equation, $m$: integer and $q=h^2$: parameter

A&S Ref:

20.2.26

Referenced by:

§28.6(i), §28.6(i), Erratum (V1.1.10) for Sections 28.6(i), 28.6(ii), 28.8(i), 28.8(ii)

Permalink:

http://dlmf.nist.gov/28.6.E14

Encodings:

pMML, png, TeX

See also:

Annotations for §28.6(i), §28.6 and Ch.28

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8: Bibliography E

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The penetration of a potential barrier by electrons. Phys. Rev. 35 (11), pp. 1303–1309.

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External Links:

Document, ZentralBlatt

Referenced by:

§15.18.

Encodings:

BibTeX

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Riemann’s Zeta Function. Academic Press, New York-London.

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Notes:

Pure and Applied Mathematics, Vol. 58. Reprinted by Dover Publications Inc., Mineola, NY, 2001.

External Links:

MathReview (Bruce C. Berndt), ZentralBlatt

Referenced by:

Ch.25.

Encodings:

BibTeX

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Higher Transcendental Functions. Vol. II. McGraw-Hill Book Company, Inc., New York-Toronto-London.

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Notes:

Reprinted by Robert E. Krieger Publishing Co. Inc., 1981. Table errata: Math. Comp. v. 41 (1983), no. 164, p. 778, v. 36 (1981), no. 153, p. 315, v. 30 (1976), no. 135, p. 675, v. 29 (1975), no. 130, p. 670, v. 26 (1972), no. 118, p. 598, v. 25 (1971), no. 113, p. 199, v. 24 (1970), no. 109, p. 239, v. 17 (1963), no. 84, p. 485.

External Links:

MathReview (E. T. Copson), ZentralBlatt

Referenced by:

§10.22(iv), §10.22(vi), §10.23(iii), §10.23(iii), §10.23(iv), §10.32(i), §10.32(iii), §10.32(iv), §10.43(iv), §10.43(vi), §10.44(iv), §10.60(iv), §10.9(i), §10.9(iii), §10.9(iv), §11.10(vi), §11.4(i), Ch.11, §12.12, §12.12, §12.13(i), §12.5(iv), Ch.12, §18.16(vi), (18.17.21_1), §18.17(iv), §18.17(i), §18.17(viii), (18.35.1), (18.35.2), (18.35.4_5), §18.35(i), (18.5.11_1), (18.5.11_3), §18.5(ii), §18.9(iii), §19.1, §19.10(i), §19.14(ii), (19.25.40), §19.25(vi), §19.5, §19.7(ii), §19.9(i), Ch.19, §20.9(i), §22.15(ii), §23.6(iv), Ch.23, §8.13(i), §8.14, §8.3(i), §8.4, §8.6(iii), §8.7, Ch.8, Notations P, Notations P.

Encodings:

BibTeX

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Painlevé transcendent describes quantum correlation function of the $XXZ$ antiferromagnet away from the free-fermion point. J. Phys. A 29 (17), pp. 5619–5626.

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External Links:

ISSN 0305-4470, Document, MathReview (Estelle L. Basor), ZentralBlatt

Referenced by:

§32.16.

Encodings:

BibTeX

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Institutiones Calculi Integralis. Opera Omnia (1), Vol. 11, pp. 110–113.

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Referenced by:

§25.12(i).

Encodings:

BibTeX

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9: 26.9 Integer Partitions: Restricted Number and Part Size

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Table 26.9.1: Partitions $p_k\left(n\right)$.

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$n$	$k$
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6	0	1	4	7	9	10	11	11	11	11	11
7	0	1	4	8	11	13	14	15	15	15	15
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9	0	1	5	12	18	23	26	28	29	30	30
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10: Bibliography

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Asymptotic expansions of spheroidal wave functions. J. Math. Phys. Mass. Inst. Tech. 28, pp. 195–199.

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External Links:

MathReview (J. G. van der Corput), ZentralBlatt

Referenced by:

§30.9(iii).

Encodings:

BibTeX

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Complex Analysis: An Introduction of the Theory of Analytic Functions of One Complex Variable. 2nd edition, McGraw-Hill Book Co., New York.

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Notes:

A third edition was published in 1978 by McGraw-Hill, New York.

External Links:

MathReview (P. Lelong), ZentralBlatt

Referenced by:

§1.9(iii), §23.18.

Encodings:

BibTeX

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On the zeros of confluent hypergeometric functions. III. Characterization by means of nonlinear equations. Lett. Nuovo Cimento (2) 29 (11), pp. 353–358.

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External Links:

ISSN 0024-1318, MathReview (James M. Horner)

Referenced by:

§13.9(i).

Encodings:

BibTeX

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Normal forms of functions in the neighborhood of degenerate critical points. Uspehi Mat. Nauk 29 (2(176)), pp. 11–49 (Russian).

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Notes:

Collection of articles dedicated to the memory of Ivan Georgievič Petrovskiĭ (1901–1973), I. In Russian. English translation: Russian Math. Surveys, 29(1974), no. 2, pp. 10–50.

External Links:

Document, MathReview (G. R. Belickii), ZentralBlatt

Referenced by:

§36.2(i).

Encodings:

BibTeX

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Some basic hypergeometric extensions of integrals of Selberg and Andrews. SIAM J. Math. Anal. 11 (6), pp. 938–951.

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External Links:

ISSN 0036-1410, Document, MathReview (W. A. Al-Salam), ZentralBlatt

Referenced by:

§17.13, §17.13.

Encodings:

BibTeX

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