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1: 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. …

2: 26.2 Basic Definitions

… ►See Table 26.2.1 for $n=0(1)50$. … ►

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
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16	231	33	10143	50	2 04226

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3: Bibliography Y

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$L$-squared discretizations of the continuum: Radial kinetic energy and the Coulomb Hamiltonian. Phys. Rev. A 11 (4), pp. 1144–1156.

ⓘ

Referenced by:

§18.39(iv), §18.39(iv), §18.39(iv), §18.40(ii).

Encodings:

BibTeX

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Computation of the derivatives of the Riemann zeta-function in the complex domain. USSR Comput. Math. and Math. Phys. 28 (4), pp. 115–124.

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Notes:

Includes Fortran programs.

External Links:

Document, ZentralBlatt

Referenced by:

§25.18(i), §25.21(iii).

Encodings:

BibTeX

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Software for interval arithmetic: A reasonably portable package. ACM Trans. Math. Software 5 (1), pp. 50–63.

ⓘ

External Links:

ISSN 0098-3500, Document

Referenced by:

§4.48(ii).

Encodings:

BibTeX

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4: 24.2 Definitions and Generating Functions

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Table 24.2.3: Bernoulli numbers $B_n=N/D$.

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$n$	$N$	$D$	$B_n$
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$28$	$-\mathrm{2\hspace{0.33em}37494\hspace{0.33em}61029}$	$870$	$-\mathrm{2.72982\hspace{0.33em}3107}$	$\mathrm{\times 10⁷}$
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Table 24.2.4: Euler numbers $E_n$.

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$n$	$E_n$
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$28$	$\mathrm{12522\hspace{0.33em}59641\hspace{0.33em}40362\hspace{0.33em}98654\hspace{0.33em}68285}$
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Table 24.2.5: Coefficients $b_{n,k}$ of the Bernoulli polynomials $B_n\left(x\right)={\sum }_{k=0}^n{b}_{n,k}{x}^k$.

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	$k$
$n$	$0$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$	$11$	$12$	$13$	$14$	$15$
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$11$	$0$	$\frac{5}{6}$	$0$	$-\frac{11}{2}$	$0$	$11$	$0$	$-11$	$0$	$\frac{55}{6}$	$-\frac{11}{2}$	$1$
…

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Table 24.2.6: Coefficients $e_{n,k}$ of the Euler polynomials $E_n\left(x\right)={\sum }_{k=0}^n{e}_{n,k}{x}^k$.

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	$k$
$n$	$0$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$	$11$	$12$	$13$	$14$	$15$
…

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5: 11 Struve and Related Functions

Chapter 11 Struve and Related Functions

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6: Staff

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

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Gerhard Wolf, University of Duisberg-Essen, Chap. 28

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

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Simon Ruijsenaars, University of Leeds, for Chaps. 5, 28

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7: 26.6 Other Lattice Path Numbers

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Table 26.6.1: Delannoy numbers $D(m,n)$.

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$m$	$n$
	…
1	1	3	5	7	9	11	13	15	17	19	21
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5	1	11	61	231	681	1683	3653	7183	13073	22363	36365
…

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… ►

Table 26.6.2: Motzkin numbers $M(n)$.

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$n$	$M(n)$	$n$	$M(n)$	$n$	$M(n)$	$n$	$M(n)$	$n$	$M(n)$
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3	4	7	127	11	5798	15	3 10572	19	181 99284

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… ►

Table 26.6.3: Narayana numbers $N(n,k)$.

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$n$	$k$
	…
8	0	1	28	196	490	490	196	28	1
…

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… ►

Table 26.6.4: Schröder numbers $r(n)$.

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$n$	$r(n)$	$n$	$r(n)$	$n$	$r(n)$	$n$	$r(n)$	$n$	$r(n)$
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$3$	$22$	$7$	$8558$	$11$	$\mathrm{52\hspace{0.33em}93446}$	$15$	$\mathrm{39376\hspace{0.33em}03038}$	$19$	$\mathrm{323\hspace{0.33em}67243\hspace{0.33em}17174}$

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8: 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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Table 27.2.2: Functions related to division.

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$n$	$\varphi \left(n\right)$	$d\left(n\right)$	$\sigma \left(n\right)$	$n$	$\varphi \left(n\right)$	$d\left(n\right)$	$\sigma \left(n\right)$	$n$	$\varphi \left(n\right)$	$d\left(n\right)$	$\sigma \left(n\right)$	$n$	$\varphi \left(n\right)$	$d\left(n\right)$	$\sigma \left(n\right)$
…
2	1	2	3	15	8	4	24	28	12	6	56	41	40	2	42
3	2	2	4	16	8	5	31	29	28	2	30	42	12	8	96
…
11	10	2	12	24	8	8	60	37	36	2	38	50	20	6	93
12	4	6	28	25	20	3	31	38	18	4	60	51	32	4	72
…

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9: 28 Mathieu Functions and Hill’s Equation

Chapter 28 Mathieu Functions and Hill’s Equation

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

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