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1: 3.4 Differentiation

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$$B_{-1}^7=-\frac{1}{240}(144-360t-48t^2+260t^3-45t^4-30t^5+7t^6),$$

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$$B_0^7=-\frac{1}{144}(36+392t-147t^2-224t^3+70t^4+24t^5-7t^6),$$

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$$B_1^7=\frac{1}{144}(144+216t-264t^2-156t^3+85t^4+18t^5-7t^6),$$

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2: 12.12 Integrals

… ►For compendia of integrals see Erdélyi et al. (1953b, v. 2, pp. 121–122), Erdélyi et al. (1954a, b, v. 1, pp. 60–61, 115, 210–211, and 336; v. 2, pp. 76–80, 115, 151, 171, and 395–398), Gradshteyn and Ryzhik (2000, §7.7), Magnus et al. (1966, pp. 330–331), Marichev (1983, pp. 190–191), Oberhettinger (1974, pp. 144–145), Oberhettinger (1990, pp. 106–108 and 192), Oberhettinger and Badii (1973, pp. 181–185), Prudnikov et al. (1986b, pp. 36–37, 155–168, 243–246, 289–290, 327–328, 419–420, and 619), Prudnikov et al. (1992a, §3.11), and Prudnikov et al. (1992b, §3.11). …

3: Bibliography G

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Asymptotics and bounds for the zeros of Laguerre polynomials: A survey. J. Comput. Appl. Math. 144 (1-2), pp. 7–27.

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External Links:

ISSN 0377-0427, Document, MathReview (M. E. Muldoon), ZentralBlatt

Referenced by:

§18.16(iv), §18.16(iv), §18.16(vi).

Encodings:

BibTeX

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Algorithm 222: Incomplete beta function ratios. Comm. ACM 7 (3), pp. 143–144.

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Notes:

Variable-precision Algol program. For a Certification see same journal 7 (1964), p. 244.

External Links:

ISSN 0001-0782, Document, Certification

Referenced by:

§8.28(iv).

Encodings:

BibTeX

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The non-symmetric Wilson polynomials are the Bannai-Ito polynomials. Proc. Amer. Math. Soc. 144 (12), pp. 5217–5226.

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External Links:

ISSN 0002-9939, Link, MathReview (Raj Wilson), ZentralBlatt

Referenced by:

§18.28(xi).

Encodings:

BibTeX

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4: 24.16 Generalizations

… ►For this and other properties see Milne-Thomson (1933, pp. 126–153) or Nörlund (1924, pp. 144–162). …

5: Bibliography N

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Askey-Wilson polynomials: an affine Hecke algebra approach. In Laredo Lectures on Orthogonal Polynomials and Special Functions, Adv. Theory Spec. Funct. Orthogonal Polynomials, pp. 111–144.

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External Links:

MathReview (V. L. Deshpande), ZentralBlatt

Referenced by:

§18.38(iii).

Encodings:

BibTeX

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6: Bibliography S

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Quantum Chaos, Symmetry and Zeta Functions. Lecture I, Quantum Chaos. In Current Developments in Mathematics, 1997 (Cambridge, MA), R. Bott (Ed.), pp. 127–144.

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External Links:

MathReview (Shin-ya Koyama), ZentralBlatt

Referenced by:

§25.17.

Encodings:

BibTeX

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Chebyshev expansions for the error and related functions. Math. Comp. 32 (144), pp. 1232–1240.

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External Links:

FullText, Document, MathReview (L. Fox), ZentralBlatt

Referenced by:

3rd item.

Encodings:

BibTeX

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About von Staudt congruences for Bernoulli numbers. Comment. Math. Univ. St. Paul. 48 (2), pp. 137–144.

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External Links:

ISSN 0010-258X, MathReview (Arnold M. Adelberg), ZentralBlatt

Referenced by:

§24.10(ii).

Encodings:

BibTeX

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On the calculation of the inverse of the error function. Math. Comp. 22 (101), pp. 144–158.

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External Links:

FullText, MathReview, ZentralBlatt

Referenced by:

§7.17(ii).

Encodings:

BibTeX

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7: 3.3 Interpolation

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$$A_0^7=\frac{1}{144}(t^2-1)(t-4)(t^2-4)(t^2-9),$$

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$$A_1^7=-\frac{1}{144}t(t+1)(t-4)(t^2-4)(t^2-9),$$

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8: Bibliography

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Some series of the zeta and related functions. Analysis (Munich) 18 (2), pp. 131–144.

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External Links:

ISSN 0174-4747, MathReview (Jack Quine), ZentralBlatt

Referenced by:

(25.11.37), (25.11.38), (25.11.39), (25.11.40), §25.11, §25.11(xi), (25.8.1), (25.8.4), §25.8.

Encodings:

BibTeX

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Periodic Differential Equations. An Introduction to Mathieu, Lamé, and Allied Functions. International Series of Monographs in Pure and Applied Mathematics, Vol. 66, Pergamon Press, The Macmillan Co., New York.

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External Links:

MathReview (A. Erdélyi), ZentralBlatt

Referenced by:

§28.1, §28.1, §28.10(i), §28.11, §28.12(ii), §28.17, §28.2(ii), §28.2(iii), §28.2(iv), §28.28(i), §28.28(ii), §28.29(i), §28.32(i), §28.32(ii), §28.4(i), §28.5(i), Ch.28, §29.1, §29.11, §29.12(i), §29.12(ii), §29.12(iii), §29.14, §29.15(ii), §29.15(ii), §29.17(i), §29.18(iii), Ch.29, §30.1, §30.10, §30.11(i), §30.11(vi), §30.2(ii), §30.4(iii), §30.6, §30.8(i), §30.8(ii), Ch.30, §31.4, §31.5, §31.9(ii), Notations F, Notations G, Notations M, Notations N.

Encodings:

BibTeX

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9: 1.11 Zeros of Polynomials

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1.11.17 $$D=16p^{4}r-4p^3{q}^2-128p^2{r}^2+144p{q}^{2}r-27q^4+256r^3.$$

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Defines:

$D$: discriminant (locally)

Symbols:

$p$ , $q$ and $r$

Permalink:

http://dlmf.nist.gov/1.11.E17

Encodings:

pMML, png, TeX

See also:

Annotations for §1.11(iii), §1.11(iii), §1.11 and Ch.1

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10: 18.12 Generating Functions

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