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1: 10 Bessel Functions

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2: Staff

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Leonard C. Maximon, George Washington University, Chaps. 10, 34

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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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3: 26.2 Basic Definitions

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

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$n$	$p\left(n\right)$	$n$	$p\left(n\right)$	$n$	$p\left(n\right)$
0	1	17	297	34	12310
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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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4: 34.7 Basic Properties: $\mathit{9}j$ Symbol

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34.7.1

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Symbols:

: $\mathit{9}j$ symbol, : $\mathit{6}j$ symbol and $j,j_r$: non-negative integers or non-negative integers plus one half.

Permalink:

http://dlmf.nist.gov/34.7.E1

Encodings:

pMML, png, TeX

See also:

Annotations for §34.7(i), §34.7 and Ch.34

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34.7.2

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Symbols:

${\delta }_{j,k}$: Kronecker delta, : $\mathit{9}j$ symbol and $j,j_r$: non-negative integers or non-negative integers plus one half.

Permalink:

http://dlmf.nist.gov/34.7.E2

Encodings:

pMML, png, TeX

See also:

Annotations for §34.7(iv), §34.7 and Ch.34

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34.7.3

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Symbols:

: $\mathit{9}j$ symbol and $j,j_r$: non-negative integers or non-negative integers plus one half.

Referenced by:

§34.9

Permalink:

http://dlmf.nist.gov/34.7.E3

Encodings:

pMML, png, TeX

See also:

Annotations for §34.7(vi), §34.7 and Ch.34

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34.7.4

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Symbols:

: $\mathit{9}j$ symbol, : $\mathit{3}j$ symbol, $j,j_r$: non-negative integers or non-negative integers plus one half. and $r$: nonnegative integer

Referenced by:

Erratum (V1.0.10) for Equation (34.7.4)

Permalink:

http://dlmf.nist.gov/34.7.E4

Encodings:

pMML, png, TeX

Errata (effective with 1.0.10):

Originally the third $\mathit{3}j$ symbol in the summation was written incorrectly as

Reported 2015-01-19 by Yan-Rui Liu

See also:

Annotations for §34.7(vi), §34.7 and Ch.34

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34.7.5

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Symbols:

: $\mathit{9}j$ symbol, : $\mathit{6}j$ symbol and $j,j_r$: non-negative integers or non-negative integers plus one half.

Permalink:

http://dlmf.nist.gov/34.7.E5

Encodings:

pMML, png, TeX

See also:

Annotations for §34.7(vi), §34.7 and Ch.34

5: 11 Struve and Related Functions

Chapter 11 Struve and Related Functions

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6: 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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7: 29 Lamé Functions

Chapter 29 Lamé Functions

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8: 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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9: 27.2 Functions

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Table 27.2.1: Primes.

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$n$	$p_n$	$p_{n+10}$	$p_{n+20}$	$p_{n+30}$	$p_{n+40}$	$p_{n+50}$	$p_{n+60}$	$p_{n+70}$	$p_{n+80}$	$p_{n+90}$
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5	11	47	97	149	197	257	313	379	439	499
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10	29	71	113	173	229	281	349	409	463	541

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Table 27.2.2: Functions related to division.

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$n$	$\varphi \left(n\right)$	$d\left(n\right)$	$\sigma \left(n\right)$	$n$	$\varphi \left(n\right)$	$d\left(n\right)$	$\sigma \left(n\right)$	$n$	$\varphi \left(n\right)$	$d\left(n\right)$	$\sigma \left(n\right)$	$n$	$\varphi \left(n\right)$	$d\left(n\right)$	$\sigma \left(n\right)$
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3	2	2	4	16	8	5	31	29	28	2	30	42	12	8	96
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8	4	4	15	21	12	4	32	34	16	4	54	47	46	2	48
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11	10	2	12	24	8	8	60	37	36	2	38	50	20	6	93
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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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