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1: Bibliography B

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Numerical evaluation of the zero-order Hankel transform using Filon quadrature philosophy. Appl. Math. Lett. 9 (5), pp. 21–26.

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External Links:

ISSN 0893-9659, Document, MathReview, ZentralBlatt

Referenced by:

§10.74(vii).

Encodings:

BibTeX

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Tables of Normalized Associated Legendre Polynomials. Pergamon Press, The Macmillan Co., Oxford-New York.

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External Links:

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

Referenced by:

3rd item.

Encodings:

BibTeX

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Rainbow over Woolsthorpe Manor. Notes and Records Roy. Soc. London 36 (1), pp. 3–11 (1 plate).

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External Links:

ISSN 0035-9149, Document, MathReview

Referenced by:

Sidebar 9.SB1.

Encodings:

BibTeX

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Irregular primes to one million. Math. Comp. 59 (200), pp. 717–722.

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External Links:

ISSN 0025-5718, FullText, MathReview (Duncan A. Buell), ZentralBlatt

Referenced by:

2nd item.

Encodings:

BibTeX

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More than 41% of the zeros of the zeta function are on the critical line. Acta Arith. 150 (1), pp. 35–64.

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External Links:

ISSN 0065-1036, Document, Link, MathReview (Timothy S. Trudgian), ZentralBlatt

Referenced by:

§25.10(ii), §25.10(ii), Erratum (V1.1.4) for Subsection 25.10(ii).

Encodings:

BibTeX

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2: 25.10 Zeros

… ►More than 41% of all the zeros in the critical strip lie on the critical line (Bui et al. (2011)). …

3: 10.73 Physical Applications

… ►See Jackson (1999, Chapter 9, §9.6), Jones (1986, Chapters 7, 8), and Lord Rayleigh (1945, Vol. I, Chapter IX, §§200–211, 218, 219, 221a; Vol. II, Chapter XIII, §272a; Chapter XV, §302; Chapter XVIII; Chapter XIX, §350; Chapter XX, §357; Chapter XXI, §369). … ►In the theory of plates and shells, the oscillations of a circular plate are determined by the differential equation ►

10.73.3 $${\nabla }^{4}W+{\lambda }^2\frac{{\partial }^{2}W}{{\partial t}^2}=0.$$

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Symbols:

$\frac{\partial f}{\partial x}$: partial derivative of $f$ with respect to $x$ and $\partial x$: partial differential of $x$

Permalink:

http://dlmf.nist.gov/10.73.E3

Encodings:

pMML, png, TeX

See also:

Annotations for §10.73(i), §10.73 and Ch.10

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4: Bibliography T

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Simplified calculation of $\mathrm{Ei}(x)$ for positive arguments, and a short table of $\mathrm{Shi}(x)$ . Math. Comp. 22 (102), pp. 448–449.

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External Links:

FullText, Document, ZentralBlatt

Referenced by:

§6.18(i).

Encodings:

BibTeX

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Numerical evaluation of exponential integral: Theis well function approximation. Journal of Hydrology 205 (1-2), pp. 38–51.

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External Links:

Document

Referenced by:

§6.18(i).

Encodings:

BibTeX

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5: Bibliography R

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Tablitsy modifitsirovannykh funktsii Besselya $K_{\frac{1}{2}+i\beta }(x)$ . “Nauka”, Moscow (Russian).

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Notes:

In Russian. Translated title: Tables of Modified Bessel Functions $K_{\frac{1}{2}+i\beta }(x)$

External Links:

MathReview, ZentralBlatt

Referenced by:

2nd item.

Encodings:

BibTeX

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Tables of the integrals and differential coefficients of $\mathrm{Gi}(+x)$ and $\mathrm{Hi}(-x)$ . Quart. J. Mech. Appl. Math. 7 (3), pp. 379–384.

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External Links:

Document, MathReview (A. Erdélyi), ZentralBlatt

Referenced by:

(9.12.30), (9.12.31), §9.12(viii), §9.16, 2nd item.

Encodings:

BibTeX

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The problem of an infinite plate under an inclined loading, with tables of the integrals of $\mathrm{Ai}(\pm \mathrm{x})$ and $\mathrm{Bi}(\pm \mathrm{x})$ . Quart. J. Mech. Appl. Math. 7 (1), pp. 1–7.

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External Links:

Document, MathReview (A. Erdélyi), ZentralBlatt

Referenced by:

§9.16, 1st item.

Encodings:

BibTeX

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6: Errata

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In the paragraph immediately below (25.10.4), it was originally stated that “more than one-third of all zeros in the critical strip lie on the critical line.” which referred to Levinson (1974). This sentence has been updated with “one-third” being replaced with “41%” now referring to Bui et al. (2011) (suggested by Gergő Nemes on 2021-08-23).

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Clarifications were made to this subsection with the addition of Equations (3.5.30_5), (3.5.33_1), (3.5.33_2), (3.5.33_3) and Table 3.5.17_5.

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The correct headings for the second and third columns of this table are $J_0\left(t\right)$ and $g(t)$, respectively. Previously these columns were mislabeled as $g(t)$ and $J_0\left(t\right)$.

$t$	$J_0(t)$	$g(t)$
0.0	1.00000 00000	1.00000 00000
0.5	0.93846 98072	0.93846 98072
1.0	0.76519 76866	0.76519 76865
2.0	0.22389 07791	0.22389 10326
5.0	$-$0.17759 67713	$-$0.17902 54097
10.0	$-$0.24593 57645	$-$0.07540 53543

Reported 2014-01-31 by Masataka Urago.

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Originally the Stirling number $s(10,6)$ was given incorrectly as 6327. The correct number is 63273.

$n$	$k$
	$0$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
10	$0$	$-\mathrm{3\hspace{0.17em}62880}$	$\mathrm{10\hspace{0.17em}26576}$	$-\mathrm{11\hspace{0.17em}72700}$	$\mathrm{7\hspace{0.17em}23680}$	$-\mathrm{2\hspace{0.17em}69325}$	$63273$	$-9450$	$870$	$-45$	$1$

Reported 2013-11-25 by Svante Janson.

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Special cases of normalization of Jacobi polynomials for which the general formula is undefined have been stated explicitly in Table 18.3.1.

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7: 24.20 Tables

§24.20 Tables

… ►In Wagstaff (2002) these results are extended to $n=60(2)152$ and $n=40(2)88$, respectively, with further complete and partial factorizations listed up to $n=300$ and $n=200$, respectively. ►For information on tables published before 1961 see Fletcher et al. (1962, v. 1, §4) and Lebedev and Fedorova (1960, Chapters 11 and 14).

8: 9.16 Physical Applications

… ►An application of the Scorer functions is to the problem of the uniform loading of infinite plates (Rothman (1954b, a)).

9: 8.26 Tables

§8.26 Tables

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§8.26(ii) Incomplete Gamma Functions

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§8.26(iii) Incomplete Beta Functions

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§8.26(iv) Generalized Exponential Integral

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Chiccoli et al. (1988) presents a short table of $E_p\left(x\right)$ for $p=-\frac{9}{2}(1)-\frac{1}{2}$, $0\le x\le 200$ to 14S.

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10: List of Tables

List of Tables