Kapteyn%20inequality

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

Referenced by:

§8.10.

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

Referenced by:

§5.6(i), §5.6(i).

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12: Bibliography L

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Inequalities and approximations for zeros of Bessel functions of small order. SIAM J. Math. Anal. 14 (2), pp. 383–388.

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ISSN 0036-1410, Document, MathReview (S. Ahmed), ZentralBlatt

Referenced by:

§10.21(iv).

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Monotonicity results and inequalities for the gamma and error functions. J. Comput. Appl. Math. 23 (1), pp. 25–33.

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

Referenced by:

§7.8.

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Further inequalities for the gamma function. Math. Comp. 42 (166), pp. 597–600.

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ISSN 0025-5718, FullText, MathReview (H. E. Fettis), ZentralBlatt

Referenced by:

§5.6(i).

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Inequalities for Bessel functions. J. Comput. Appl. Math. 15 (1), pp. 75–81.

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ISSN 0377-0427, Document, MathReview (B. D. Agrawal), ZentralBlatt

Referenced by:

§10.14.

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Inequalities for ultraspherical polynomials and the gamma function. J. Approx. Theory 40 (2), pp. 115–120.

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ISSN 0021-9045, Document, MathReview (B. R. Bhonsle), ZentralBlatt

Referenced by:

§18.14(i).

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13: 10.37 Inequalities; Monotonicity

§10.37 Inequalities; Monotonicity

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

14: 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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15: 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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$20$	$64$	$31$	$20$	$18$

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… ►Note that $p({𝒟}^{\prime }3,n)\le p(𝒟3,n)$, with strict inequality for $n\ge 9$. It is known that for $k>3$, $p(𝒟k,n)\ge p(\in A_{1,k+3},n)$, with strict inequality for $n$ sufficiently large, provided that $k=2^m-1,m=3,4,5$, or $k\ge 32$; see Yee (2004). …

16: 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).

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

Referenced by:

§10.37, §10.37.

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Inequalities involving cylindrical functions of nearly equal argument and order. Proc. Amer. Math. Soc. 5 (3), pp. 337–344.

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ISSN 0002-9939, FullText, MathReview (N. D. Kazarinoff), ZentralBlatt

Referenced by:

§10.14.

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An inequality involving Bessel functions of argument nearly equal to their order. Proc. Amer. Math. Soc. 4 (6), pp. 858–859.

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ISSN 0002-9939, FullText, MathReview (N. D. Kazarinoff), ZentralBlatt

Referenced by:

§10.14.

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

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

Referenced by:

§18.14(ii).

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17: 24.9 Inequalities

§24.9 Inequalities

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

18: Bibliography P

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An inequality for the Bessel function $J_{\nu }(\nu x)$ . SIAM J. Math. Anal. 15 (1), pp. 203–205.

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ISSN 0036-1410, Document, MathReview (L. Debnath)

Referenced by:

§10.14, §10.37.

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Automatic computation of Bessel function integrals. Comput. Phys. Comm. 25 (3), pp. 289–295.

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Notes:

Double-precision Fortran, maximum accuracy 20S.

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ISSN 0010-4655, Document, Code

Referenced by:

6th item.

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Inequalities for the zeros of the Airy functions. SIAM J. Math. Anal. 22 (1), pp. 260–267.

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External Links:

ISSN 0036-1410, Document, MathReview, ZentralBlatt

Referenced by:

§9.9(iv).

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19: 8 Incomplete Gamma and Related
Functions

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20: 28 Mathieu Functions and Hill’s Equation

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