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1: DLMF Project News

error generating summary

2: Guide to Searching the DLMF

… ►Sometimes there are distinctions between various special function names based on font style, such as the use of bold or calligraphic letters. DLMF search recognizes just the essential font differences, that is, the font style differences deemed important for the DLMF contents: … ►If you don’t specify the font style or font accessories in the query, the style and accessories won’t matter in the search, but if you specify them, they will matter. …

3: Staff

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Richard A. Askey, University of Wisconsin, Chaps. 1, 5, 16

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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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4: 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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Advances in Math Search, Proceedings 6th International Congress on Industrial and Applied Mathematics, Zürich, Switzerland, July 17, 2007.

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5: 10 Bessel 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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16	231	33	10143	50	2 04226

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7: 11 Struve and Related Functions

Chapter 11 Struve and Related Functions

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8: 29 Lamé Functions

Chapter 29 Lamé Functions

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

ⓘ

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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28.6.21 $$2^{1/2}{\mathrm{ce}}_0(z,q)=1-\frac{1}{2}q\cos 2z+\frac{1}{32}{q}^2\left(\cos 4z-2\right)-\frac{1}{128}{q}^3\left(\frac{1}{9}\cos 6z-11\cos 2z\right)+\mathrm{\cdots },$$

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Symbols:

${\mathrm{ce}}_n(z,q)$: Mathieu function, $\cos z$: cosine function, $q=h^2$: parameter and $z$: complex variable

A&S Ref:

20.2.27

Referenced by:

§28.6(ii)

Permalink:

http://dlmf.nist.gov/28.6.E21

Encodings:

pMML, png, TeX

See also:

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

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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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$n$	$\varphi \left(n\right)$	$d\left(n\right)$	$\sigma \left(n\right)$	$n$	$\varphi \left(n\right)$	$d\left(n\right)$	$\sigma \left(n\right)$	$n$	$\varphi \left(n\right)$	$d\left(n\right)$	$\sigma \left(n\right)$	$n$	$\varphi \left(n\right)$	$d\left(n\right)$	$\sigma \left(n\right)$
1	1	1	1	14	6	4	24	27	18	4	40	40	16	8	90
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3	2	2	4	16	8	5	31	29	28	2	30	42	12	8	96
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11	10	2	12	24	8	8	60	37	36	2	38	50	20	6	93
…

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