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1: Staff

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

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William P. Reinhardt, University of Washington, Chaps. 20, 22, 23

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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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2: 34.6 Definition: $\mathit{9}j$ Symbol

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34.6.1

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Defines:

: $\mathit{9}j$ symbol

Symbols:

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

Permalink:

http://dlmf.nist.gov/34.6.E1

Encodings:

pMML, png, TeX

See also:

Annotations for §34.6 and Ch.34

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34.6.2

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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.

Referenced by:

§34.13

Permalink:

http://dlmf.nist.gov/34.6.E2

Encodings:

pMML, png, TeX

See also:

Annotations for §34.6 and Ch.34

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3: 10 Bessel Functions

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4: 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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5	7	22	1002	39	31185
6	11	23	1255	40	37338
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8	22	25	1958	42	53174
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11	56	28	3718	45	89134
12	77	29	4565	46	1 05558
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5: 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

ⓘ

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

6: 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
8	0	1	5	10	15	18	20	21	22	22	22
9	0	1	5	12	18	23	26	28	29	30	30
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7: 11 Struve and Related Functions

Chapter 11 Struve and Related Functions

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8: 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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9: 29 Lamé Functions

Chapter 29 Lamé Functions

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10: 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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7	6	2	8	20	8	6	42	33	20	4	48	46	22	4	72
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11	10	2	12	24	8	8	60	37	36	2	38	50	20	6	93
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