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21: 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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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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22: Bibliography

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A harmonic mean inequality for the gamma function. J. Comput. Appl. Math. 87 (2), pp. 195–198.

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Notes:

For corrigendum see same journal v. 90 (1998), no. 2, p. 265

External Links:

ISSN 0377-0427, Document, MathReview, ZentralBlatt

Referenced by:

§5.6(i).

Encodings:

BibTeX

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A trinomial analogue of Bailey’s lemma and $N=2$ superconformal invariance. Comm. Math. Phys. 192 (2), pp. 245–260.

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External Links:

ISSN 0010-3616, Document, MathReview (Anne Schilling), ZentralBlatt

Referenced by:

§17.12.

Encodings:

BibTeX

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Bernoulli’s power-sum formulas revisited. Math. Gaz. 90 (518), pp. 276–279.

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Referenced by:

§24.4(iii).

Encodings:

BibTeX

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23: Bibliography K

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Algorithm 763: INTERVAL_ARITHMETIC: A Fortran 90 module for an interval data type. ACM Trans. Math. Software 22 (4), pp. 385–392.

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External Links:

ISSN 0098-3500, Document, GAMS (module 763; package TOMS), ZentralBlatt

Referenced by:

2nd item.

Encodings:

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Nonsymmetric Askey-Wilson polynomials as vector-valued polynomials. Appl. Anal. 90 (3-4), pp. 731–746.

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External Links:

ISSN 0003-6811, Link, MathReview (Masatoshi Iida), ZentralBlatt

Referenced by:

§18.38(iii), §18.38(iii).

Encodings:

BibTeX

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24: 3.9 Acceleration of Convergence

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Table 3.9.1: Shanks’ transformation for $s_n={\sum }_{j=1}^n{(-1)}^{j+1}{j}^{-2}$.

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$n$	$t_{n,2}$	$t_{n,4}$	$t_{n,6}$	$t_{n,8}$	$t_{n,10}$
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3	0.82300 13550 14	0.82247 78118 35	0.82246 72851 83	0.82246 70397 56	0.82246 70335 90
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25: 25.6 Integer Arguments

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$\zeta \left(4\right)={\displaystyle \frac{{\pi }^4}{90}},$

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26: 26.6 Other Lattice Path Numbers

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

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$n$	$r(n)$	$n$	$r(n)$	$n$	$r(n)$	$n$	$r(n)$	$n$	$r(n)$
$0$	$1$	$4$	$90$	$8$	$41586$	$12$	$\mathrm{272\hspace{0.33em}97738}$	$16$	$\mathrm{2\hspace{0.33em}09271\hspace{0.33em}56706}$
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27: Bibliography V

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Expansion of vacuum magnetic fields in toroidal harmonics. Comput. Phys. Comm. 81 (1-2), pp. 74–90.

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External Links:

Document

Referenced by:

§14.31(i).

Encodings:

BibTeX

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28: Bibliography G

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An improved algorithm and a Fortran 90 module for computing the conical function $P_{-1/2+i\tau }^m(x)$ . Comput. Phys. Commun. 183 (3), pp. 794–799.

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External Links:

ISSN 0010-4655, Document, Link, MathReview Entry, ZentralBlatt

Referenced by:

5th item, §14.32.

Encodings:

BibTeX

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29: Bibliography T

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Atlas for Computing Mathematical Functions: An Illustrated Guide for Practitioners. John Wiley & Sons Inc., New York.

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Notes:

With CD-ROM containing a large collection of mathematical function software written in Fortran 90 and Mathematica (an edition with the same software in C and Mathematica exists also). The functions are computed for real variables only. Maximum accuracy 12D.

External Links:

ISBN 0-471-18171-4, MathReview, ZentralBlatt

Referenced by:

§19.36(ii), § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index.

Encodings:

BibTeX

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30: 1.13 Differential Equations

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