Szegő–Szász inequality

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1: 18.14 Inequalities

§18.14 Inequalities

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Legendre

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Jacobi

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Szegő–Szász Inequality

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2: 1.7 Inequalities

§1.7 Inequalities

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Cauchy–Schwarz Inequality

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Minkowski’s Inequality

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Cauchy–Schwarz Inequality

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§1.7(iv) Jensen’s Inequality

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3: Bibliography S

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Norm inequalities for a certain class of $C^{\mathrm{\infty }}$ functions. Israel J. Math. 10, pp. 364–372.

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External Links:

Document, MathReview (V. Ganapathy Iyer), ZentralBlatt

Referenced by:

§24.17(ii).

Encodings:

BibTeX

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Bounds for ratios of modified Bessel functions and associated Turán-type inequalities. J. Math. Anal. Appl. 374 (2), pp. 516–528.

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External Links:

ISSN 0022-247X, Document, FullText, MathReview (Beyza Caliskan Aslan), ZentralBlatt

Referenced by:

§10.37, §10.37.

Encodings:

BibTeX

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On inequalities of the Turán type. Math. Scand. 2, pp. 65–73.

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External Links:

ISSN 0025-5521, FullText, MathReview (G. Szegő), ZentralBlatt

Referenced by:

§18.14(ii).

Encodings:

BibTeX

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On the relative extrema of ultraspherical polynomials. Boll. Un. Mat. Ital. (3) 5, pp. 125–127.

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External Links:

MathReview (A. Erdélyi), ZentralBlatt

Referenced by:

§18.14(iii).

Encodings:

BibTeX

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On the relative extrema of the Hermite orthogonal functions. J. Indian Math. Soc. (N.S.) 15, pp. 129–134.

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External Links:

MathReview (J. Todd), ZentralBlatt

Referenced by:

§18.14(i).

Encodings:

BibTeX

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4: Edward Neuman

… ►Neuman has published several papers on approximations and expansions, special functions, and mathematical inequalities. …

5: 4.32 Inequalities

§4.32 Inequalities

… ►For these and other inequalities involving hyperbolic functions see Mitrinović (1964, pp. 61, 76, 159) and Mitrinović (1970, p. 270).

6: 6.8 Inequalities

§6.8 Inequalities

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7: Bibliography Q

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Some inequalities of the incomplete gamma and related functions. Z. Anal. Anwendungen 18 (3), pp. 793–799.

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External Links:

ISSN 0232-2064, FullText, MathReview (Richard B. Paris), ZentralBlatt

Referenced by:

§8.10.

Encodings:

BibTeX

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A new lower bound in the second Kershaw’s double inequality. J. Comput. Appl. Math. 214 (2), pp. 610–616.

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External Links:

ISSN 0377-0427, Document, FullText, MathReview (Mehdi Hassani), ZentralBlatt

Referenced by:

§5.6(i), §5.6(i).

Encodings:

BibTeX

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8: 10.37 Inequalities; Monotonicity

§10.37 Inequalities; Monotonicity

… ►For sharper inequalities when the variables are real see Paris (1984) and Laforgia (1991). …

9: 7.8 Inequalities

§7.8 Inequalities

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7.8.7 $x>0$.

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Symbols:

$F\left(z\right)$: Dawson’s integral, $dx$: differential of $x$ , $\mathrm{e}$: base of natural logarithm, $\sinh z$: hyperbolic sine function, $\int$: integral and $x$: real variable

Referenced by:

Erratum (V1.1.5) for Additions

Permalink:

http://dlmf.nist.gov/7.8.E7

Encodings:

pMML, png, TeX

Addition (effective with 1.1.5):

A new inequality was added.

See also:

Annotations for §7.8 and Ch.7

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7.8.8 $x>0$.

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Symbols:

$\pi$: the ratio of the circumference of a circle to its diameter, $\mathrm{erf}z$: error function, $\mathrm{e}$: base of natural logarithm and $x$: real variable

Source:

Pólya (1949, (1.5))

Referenced by:

§7.8, Erratum (V1.0.17) for Equation (7.8.8)

Permalink:

http://dlmf.nist.gov/7.8.E8

Encodings:

pMML, png, TeX

Addition (effective with 1.0.17):

This inequality was added. It is Pólya (1949, (1.5)). Note that it is a special case of (8.10.11).

Suggested by Roberto Iacono

See also:

Annotations for §7.8 and Ch.7

10: 24.9 Inequalities

§24.9 Inequalities

►Except where otherwise noted, the inequalities in this section hold for $n=1,2,\mathrm{\dots }$. …