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31: 10.75 Tables

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Achenbach (1986) tabulates $J_0\left(x\right)$, $J_1\left(x\right)$, $Y_0\left(x\right)$, $Y_1\left(x\right)$, $x=0(.1)8$, 20D or 18–20S.

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Makinouchi (1966) tabulates all values of $j_{\nu ,m}$ and $y_{\nu ,m}$ in the interval $(0,100)$, with at least 29S. These are for $\nu =0(1)5$, 10, 20; $\nu =\frac{3}{2}$, $\frac{5}{2}$; $\nu =m/n$ with $m=1(1)n-1$ and $n=3(1)8$, except for $\nu =\frac{1}{2}$.

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Abramowitz and Stegun (1964, Chapter 11) tabulates ${\int }_0^x{J}_0\left(t\right)dt$, ${\int }_0^x{Y}_0\left(t\right)dt$, $x=0(.1)10$, 10D; ${\int }_0^x{t}^{-1}(1-J_0\left(t\right))dt$, ${\int }_x^{\mathrm{\infty }}{t}^{-1}{Y}_0\left(t\right)dt$, $x=0(.1)5$, 8D.

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Leung and Ghaderpanah (1979), tabulates all zeros of the principal value of $K_n\left(z\right)$, for $n=2(1)10$, 29S.

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Abramowitz and Stegun (1964, Chapter 11) tabulates ${\mathrm{e}}^{-x}{\int }_0^x{I}_0\left(t\right)dt$, ${\mathrm{e}}^x{\int }_x^{\mathrm{\infty }}{K}_0\left(t\right)dt$, $x=0(.1)10$, 7D; ${\mathrm{e}}^{-x}{\int }_0^x{t}^{-1}(I_0\left(t\right)-1)dt$, $x{\mathrm{e}}^x{\int }_x^{\mathrm{\infty }}{t}^{-1}{K}_0\left(t\right)dt$, $x=0(.1)5$, 6D.

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32: 26.6 Other Lattice Path Numbers

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

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$m$	$n$
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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 26.6.4: 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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$2$	$6$	$6$	$1806$	$10$	$\mathrm{10\hspace{0.33em}37718}$	$14$	$\mathrm{7453\hspace{0.33em}87038}$	$18$	$\mathrm{60\hspace{0.33em}03188\hspace{0.33em}53926}$
$3$	$22$	$7$	$8558$	$11$	$\mathrm{52\hspace{0.33em}93446}$	$15$	$\mathrm{39376\hspace{0.33em}03038}$	$19$	$\mathrm{323\hspace{0.33em}67243\hspace{0.33em}17174}$

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33: Bibliography H

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On the distribution of the zeros of generalized Airy functions. Math. Comp. 29 (131), pp. 863–877.

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External Links:

FullText, MathReview (F. W. J. Olver), ZentralBlatt

Referenced by:

§9.13(i).

Encodings:

BibTeX

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Inverse virial symmetry of diatomic potential curves. J. Chem. Phys. 109 (1), pp. 11–19.

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External Links:

Document

Referenced by:

§15.18.

Encodings:

BibTeX

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Error bounds for asymptotic approximations of zeros of Hankel functions occurring in diffraction problems. J. Mathematical Phys. 11 (8), pp. 2501–2504.

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External Links:

Document, MathReview (F. W. J. Olver), ZentralBlatt

Referenced by:

§10.21(xiv).

Encodings:

BibTeX

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Algorithm 395: Student’s t-distribution. Comm. ACM 13 (10), pp. 617–619.

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Notes:

Includes Algol program, maximum accuracy 11S. For Remarks see ACM Trans. Math. Software 5(1979) and 7(1981)

External Links:

ISSN 0001-0782, Document, Remark 1, Remark 2

Referenced by:

§8.28(iv).

Encodings:

BibTeX

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An explicit formula for Bernoulli numbers. Rep. Fac. Sci. Technol. Meijo Univ. 29, pp. 1–6.

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External Links:

ZentralBlatt

Referenced by:

§24.6.

Encodings:

BibTeX

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34: 34.9 Graphical Method

… ►For specific examples of the graphical method of representing sums involving the $\mathit{3}j,\mathit{6}j$, and $\mathit{9}j$ symbols, see Varshalovich et al. (1988, Chapters 11, 12) and Lehman and O’Connell (1973, §3.3).

35: Richard B. Paris

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11 Struve and Related Functions

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36: 26.5 Lattice Paths: Catalan Numbers

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Table 26.5.1: Catalan numbers.

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$n$	$C\left(n\right)$	$n$	$C\left(n\right)$	$n$	$C\left(n\right)$
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4	14	11	58786	18	4776 38700
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37: 26.10 Integer Partitions: Other Restrictions

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Table 26.10.1: Partitions restricted by difference conditions, or equivalently with parts from $A_{j,k}$.

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	$p(𝒟,n)$	$p(𝒟2,n)$	$p(𝒟2,\in T,n)$	$p({𝒟}^{\prime }3,n)$
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$11$	$12$	$7$	$4$	$5$
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$13$	$18$	$10$	$6$	$7$
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$16$	$32$	$17$	$11$	$10$
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$18$	$46$	$23$	$15$	$14$
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$20$	$64$	$31$	$20$	$18$

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38: 25.20 Approximations

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Cody et al. (1971) gives rational approximations for $\zeta \left(s\right)$ in the form of quotients of polynomials or quotients of Chebyshev series. The ranges covered are $0.5\le s\le 5$, $5\le s\le 11$, $11\le s\le 25$, $25\le s\le 55$. Precision is varied, with a maximum of 20S.

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39: 24.20 Tables

… ►For information on tables published before 1961 see Fletcher et al. (1962, v. 1, §4) and Lebedev and Fedorova (1960, Chapters 11 and 14).

40: 26.7 Set Partitions: Bell Numbers

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Table 26.7.1: Bell numbers.

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$n$	$B\left(n\right)$	$n$	$B\left(n\right)$
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1	1	11	6 78570
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8	4140	18	68 20768 06159
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